Driving apparatus and method for modular multi-level converter

ABSTRACT

The present invention relates to a driving method for a modular multi-level converter. The driving method include inputting a current reference value (i* pj2 ) of the upper valve of the modular multi-level converter, measuring a current value (i pj2 ) of the valve, calculating an error value (err pj2 ) between the current reference value and the measured current value of the upper valve, measuring a DC link voltage value (V dc2 ) of the modular multi-level converter, measuring a AC-grid voltage value (E sj ) of the modular multi-level converter, and calculating a voltage reference value (u* pj2 ) using the current reference value (i* pj2 ), the measured current value (i pj2 ), the error value (err pj2 ), the DC link voltage value (V dc2 ), and the AC-grid voltage value (E sj ).

CROSS-REFERENCE TO RELATED APPLICATION

This application claims under 35 U.S.C. §119(a) the benefit of KoreanPatent Application No. 10-2014-0015446 filed Feb. 11, 2014, the entirecontents of which are incorporated herein by reference.

BACKGROUND

(a) Technical Field

The present invention relates to a driving apparatus and method for amodular multi-level converter. More particularly, it relates to adriving apparatus and method for controlling submodules by an uppervalve or a lower valve of a valve branch taking charge of each phase.

(b) Background Art

When energy needs to be transported from an offshore wind farm to a mainland using a submarine cable of about 100 kilometers or more, it isknown that the High Voltage Direct-Current (HVDC) transmission is muchmore economical than the High Voltage Alternating-Current (HVAC)transmission in terms of energy transportation cost.

The HVDC transmission is known as an appropriate method particularly forinternational power transaction (energy trade) in which countries mayuse different frequencies and voltages. Also, as it is demonstrated thatthe High Voltage Direct-Current (HVDC) transmission is much moreeconomical than the High Voltage Alternating-Current (HVAC) transmissionin terms of energy transportation cost even when an energy bottleneckphenomenon occurs due to the extensive energy consumption in downtownsthat are densely populated areas, new attention is being given to theHVDC transmission.

Particularly, when solar energy and wind energy abundantly distributedin the African continent can be developed and transported to theEuropean continent, the new and renewable energy share can besignificantly increased in Europe. Thus, this technology is mostdeveloped in Europe. Also, the new and renewable energy market is beingrapidly growing in China that needs to transport large-capacityhydroelectric power stations to large cities away therefrom by about1,000 kilometers and can produce energy from deserts.

When the HVDC transmission systems are classified according to the typeof the converter, the HVDC transmission systems may be classified intoan HVDC transmission system having a current-type converter and an HVDCtransmission system having a voltage-type converter. The presentdisclosure relates to a voltage-type converter, and more particularly,to a modular multi-level converter among the voltage-type converters.

In the modular multi-level converter, a unit submodule is manufacturedusing an Insulated Gate Bipolar Transistor (IGBT) with a low voltagespecification, and the submodules are stacked in series to form a stackstructure with a withstanding voltage ability with respect to a highvoltage of hundreds of KVs. Also, the modular multi-level converter isallowed to have a variety of voltage levels according to the number ofsubmodules stacked in series.

In addition, the modular multi-level converter can perform independentcontrol of active power and reactive power which cannot be implementedin a HVDC transmission system having a current-type converter, and neednot together supply reactive power corresponding to 50% of active powerin order to transmit active power. Also, each of converters located atthe both ends of a high DC voltage can be stably controlled withoutinformation on the counter converter, and the transportation directionof active power can be simply controlled by changing only the currentdirection without a process of re-determining the magnitude of voltagesat the both ends.

However, due to its structure, the modular multi-level converter for theHVDC transmission has limitations that the current-type converter doesnot have.

In other words, since the capacity voltage in the submodule is notuniform and a resultant voltage of an upper valve voltage and a lowervalve voltage is not the same as a DC link voltage, there arelimitations in that a circulating current component flowing in themulti-level converter exists. Also, a harmonic may be induced in a highvoltage DC-grid, or a harmonic is contained in active power of anAlternating Current (AC) grid.

In order to overcome these limitations, various methods have beenproposed. However, when an accident such as one-phase earthed occurs,the AC-grid voltage becomes an unbalance voltage state. In thiscondition, the circulating current is not suppressed, or a harmonic isinduced in the DC-grid. Also, a harmonic is contained in active power ofthe AC-grid, showing that the control characteristics are still notstrong.

Also, a typical control method for the HVDC transmission system with amodular multi-level converter requires an upper controller to perform alarge amount of operation, and is difficult to implement in a ValveController (VC). Accordingly, the typical control method for the HVDCtransmission system is not suitable for improvement of the operationspeed. Specifically, since a current reference value derived from anactive and reactive power controller and a current reference valuederived from a circulating current suppression controller use a phasecurrent, or use an expression of the phase current transformed into ad-q coordinate plane, the typical control method is suitable toimplement the controller by phase unit but is difficult to implement ineach valve control, making it difficult to improve the operation speed.

(c) Prior Art

Non-Patent

(Non-patent Document 2) A circulating current suppression methodpublished by Qingrui Tu [IEEE Trans. on Power Delivery, vol. 26, 2011]discloses a method of suppressing a circulating current of a negativesequence component when references of the 3-phase voltage arecompensated, using an output value that allows a d-axis circulatingcurrent component and a q-axis circulating current component rotating−2θ_(s) in a negative sequence order (R>T>S), not flowing into a phaseof the AC system, flowing only between a upper valve controller and anlower valve controller of each phase, and expressed in a rotatingcoordinate system to become “0”, where a circulating current has afrequency two times larger than a AC-grid frequency. However, thismethod is good in controller characteristics when the power systemvoltage is in 3-phase balance condition, but is not good in controlcharacteristics when the system voltage is under an unbalance condition.

(Non-patent Document 3) FIG. 20 is a view illustrating a method proposedby Qingrui Tu, which shows one of typical circulating currentsuppression methods.

(Non-patent Document 4) A circulating current suppression methodpublished by Qingrui Tu [IEEE Trans. on Power Delivery, vol. 27, 2012]can be used both when the system voltage is in 3-phase balance and whenthe system voltage is under the unbalance condition. He demonstratedthat power of a zero sequence component is additionally generated ineach valve when a modular multi-level converter for High VoltageDirect-Current (HVDC) transmission operates under 3-phase unbalancecondition of the system voltage. In this method, the upper valvevoltages and the lower valve voltages of each phase are added up, andthen are divided by three to acquire an average component and define theaverage component as a zero sequence component of the circulatingcurrent. An intermediate compensation value for allowing the zerosequence component of the circulating current to become “0” is acquiredby applying a resonant controller having a resonant frequency 2ω_(s) ata branch. The intermediate compensation value is added to an outputvalue for suppressing the negative sequence component to compensate fora phase voltage reference value (PWM input value). This method is shownin FIG. 4.

(Non-patent Document 5) However, although this method shows goodcharacteristics in terms of proposing a method for suppressing bothcirculating current of the negative sequence component and circulatingcurrent of the zero-sequence component, the transient statecharacteristics are not good at a start point where unbalance occurs inthe system voltage. Also, there is a complexity that can be implementedonly when the positive sequence component, negative sequence component,and the zero-sequence component are all known. Particularly, there is alimitation in that a harmonic component in addition to a DC component ismuch included in a current waveform flowing on a high voltage DC line.

(Non-patent Document 6) FIG. 19 is a view illustrating another exampleof typical circulating current suppression methods, proposed by AntoniosAnotonopoulos and Maryam Saeedifard. A region marked by a box shows amethod proposed by Antonious Anotonopoulos, and the other region shows amethod proposed by Maryam Saeedifard.

(Non-patent Document 7) When a typical method is analyzed in astructural aspect of algorithm, it cannot be seen that the algorithmconfiguration developed after Antonios Anotonopoulos [Power Electronicsand Application, EPE '09, 2009] is focused on the implementation in adistributed control system. A current reference value is generated froman active power and reactive power controller, and then a phase voltagereference value is generated through a current controller that allowsthe current reference value to be converged. Thereafter, when a voltagecomponent that suppresses an AC component of the circulating current isgenerated and compensated, voltage reference values with respect to eachvalve can be calculated. Accordingly, this method has a structureinappropriate to perform the control algorithm by using independentvalve controller.

(Non-patent Document 8) The modular multi-level converter for the HVDCtransmission system configures a current controller using a currentflowing in each phase, performs a process of suppressing the circulatingcurrent, and then determines each valve voltage reference value. Whenthe valve voltage reference value is determined, the number ofsubmodules to be turned on/off for each valve is determined, and thesubmodule voltage is smoothed. This method was significantly developedby Antonios Antonopoulous (2009). Also, regarding the unbalanced systemvoltage condition as well, a current controlling method capable ofeffectively and quickly controlling the active power (or the DC_linkconstant voltage control) and the reactive power was greatly developedby Maryam Saeedifard (2010), which is shown in FIG. 19.

(Non-patent Document 9) FIG. 21 is a view illustrating a control devicefor implementing a variety of typical methods described above.

(Non-patent Document 10) In FIG. 21, every value includes an exclusivevalve controller 2, and a station controller 1 is disposed over sixvalve controllers 2. FIG. 21 is a view illustrating an analysis of aroll allocation regarding a typical method. As shown in FIG. 21, thereare many tasks for the station controller 1 to commonly perform androles that the valve controller 2 independently performs are limited toa part of tasks. Accordingly, this structure is not appropriate for adistributed control system.

The above information disclosed in this Background section is only forenhancement of understanding of the background of the invention andtherefore it may contain information that does not form the prior artthat is already known in this country to a person of ordinary skill inthe art.

SUMMARY OF THE DISCLOSURE

The present invention provides a driving apparatus and method for amodular multi-level converter, which can implement current control andcirculating current suppression control using current flowing in sixvalves.

The present invention also provides a driving apparatus and method for amodular multi-level converter, which can perform distributed controlthrough a parallel operation of each valve controller.

In one aspect, the present invention provides a driving method for amodular multi-level converter that converts an alternating current (AC)into a direct current (DC) or converts a DC into an AC using the modularmulti-level converter with a plurality of submodules stacked to deliverpower in an AC system, the modular multi-level converter comprising aplurality of valves independently driven and an upper valve that is oneof valve branches comprising the valves, the method comprising:inputting a current reference value (i*_(pj2)) of the upper valve of themodular multi-level converter; measuring a current value (i_(pj2)) ofthe valve; calculating an error value (err_(pj2)) between the currentreference value and the measured current value of the upper valve;measuring a DC link voltage value (V_(dc2)) of the modular multi-levelconverter; measuring a AC-grid voltage value (E_(sj)) of the modularmulti-level converter; and calculating a voltage reference value(u*_(pj2)) using the current reference value (i*_(pj2)), the measuredcurrent value (i_(pj2)), the error value (err_(pj2)), the DC linkvoltage value (V_(dc2)), and the AC-grid voltage value (E_(sj)).

In an exemplary embodiment, the driving method may further includecalculating a parameter variation value ({circumflex over (l)}_(pj2)) ofa circulating current suppression inductor of the modular multi-levelconverter between the measuring of the AC-grid voltage (E_(sj)) of themodular multi-level converter and calculating of the voltage referencevalue (u*_(pj2)) using the current reference value, the measured currentvalue, the error value, the DC link voltage value, and the systemvoltage value.

In another exemplary embodiment, the calculating of the parametervariation value ({circumflex over (l)}_(pj2)) of a circulating currentsuppression inductor of the modular multi-level converter may include:obtaining a differential value of the parameter variation value of thecirculating current suppression inductor using the following equation:

{circumflex over (l)}_(pj2)=−m₁err_(pj2); and integrating thedifferential value of the parameter variation value of the circulatingcurrent suppression inductor. Here,

m₁ may be a predetermined tuning constant.

In still another exemplary embodiment, the calculating of the voltagereference value (u*_(pj2)) using the current reference value (i*_(pj2)),the measured current value (i_(pj2)), the error value (err_(pj2)), theDC link voltage value (V_(dc2)), the AC-grid voltage value (E_(sj)), andthe parameter variation value ({circumflex over (l)}_(pj2)) of thecirculating current suppression inductor may include calculating thevoltage reference value (u*_(pj2)) using the following equation:

$u_{{pj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - \left\{ {{P\left( {err}_{{pj}\; 2} \right)} + {R_{1}\left( {err}_{{pj}\; 2} \right)} + {R_{2}\left( {err}_{{pj}\; 2} \right)}} \right\} + \left\{ {L_{s}{\hat{l}}_{{pj}\; 2}} \right\}}$

In yet another exemplary embodiment, the calculating of the voltagereference value (u*_(pj2)) using the current reference value (i*_(pj2)),the measured current value (i_(pj2)), the error value (err_(pj2)), theDC link voltage value (V_(dc2)), the AC-grid voltage value (E_(sj)), andthe parameter variation value ({circumflex over (l)}_(pj2)) of thecirculating current suppression inductor may include calculating thevoltage reference value (u*_(pj2)) using the following equation:

$u_{{pj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - \left\{ {{P\left( {err}_{{pj}\; 2} \right)} + {R_{1}\left( {err}_{{pj}\; 2} \right)} + {R_{2}\left( {err}_{{pj}\; 2} \right)}} \right\} - \left\{ {{L_{s}i_{{pj}\; 2}^{*}} - {L_{s}{\hat{l}}_{{pj}\; 2}}} \right\}}$

In still yet another exemplary embodiment, the calculating of thevoltage reference value (u*_(pj2)) using the current reference value(i*_(pj2)), the measured current value (i_(pj2)), the error value(err_(pj2)), the DC link voltage value (V_(dc2)), and the AC-gridvoltage value (E_(sj)) may include calculating the voltage referencevalue (u*_(pj2)) using the following equation:

$u_{{pj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - {\left\{ {{P\left( {err}_{{pj}\; 2} \right)} + {R_{1}\left( {err}_{{pj}\; 2} \right)} + {R_{2}\left( {err}_{{pj}\; 2} \right)}} \right\}.}}$

In a further exemplary embodiment, the calculating of the voltagereference value (u*_(pj2)) using the current reference value (i*_(pj2)),the measured current value (i_(pj2)), the error value (err_(pj2)), theDC link voltage value (V_(dc2)), and the AC-grid voltage value (E_(sj)),an sgn function may include calculating the voltage reference value(u*_(pj2)) using the following equation:

$u_{{pj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - \left\{ {{P\left( {err}_{{pj}\; 2} \right)} + {R_{1}\left( {err}_{{pj}\; 2} \right)} + {R_{2}\left( {err}_{{pj}\; 2} \right)}} \right\} - {\left\{ {\rho_{{pj}\; 2}{{sgn}\left( {err}_{{pj}\; 2} \right)}} \right\}.}}$

Here, the sign function may denote a sign function operated by thefollowing equations:

sgn(err _(pj2))=1(err _(pj2)>0)

sgn(err _(pj2))=0(err _(pj2)≦0)

and ρ_(pj2) may denote a proportional gain.

In another further exemplary embodiment, the calculating of the voltagereference value (u*_(pj2)) using the current reference value (i*_(pj2)),the measured current value (i_(pj2)), the error value (err_(pj2)), theDC link voltage value (V_(dc2)), the AC-grid voltage value (E_(sj)), andan sgn function may include calculating the voltage reference value(u*_(pj2)) using the following equation:

${u_{{pj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - \left\{ {{P\left( {err}_{{pj}\; 2} \right)} + {R_{1}\left( {err}_{{pj}\; 2} \right)} + {R_{2}\left( {err}_{{pj}\; 2} \right)}} \right\} - \left\{ {\rho_{{pj}\; 2}{{sgn}\left( {err}_{{pj}\; 2} \right)}} \right\}}},$

Here, the sign function may denote a sign function operated by thefollowing equations:

sgn(err _(pj2))=1(err _(pj2)>0)

sgn(err _(pj2))=0(err _(pj2)≦0)

ρ_(pj2) may denote a proportional gain. Also, L_(s) may denote acirculating current suppression inductor of the upper valve.

In still another further exemplary embodiment, P(err_(pj2)),R₁(err_(pj2)), and R₂(err_(pj2)) may be calculated using the followingequations:

P(err_(pj 2)) = (K_(p))err_(pj 2)${{R_{1}\left( {err}_{{pj}\; 2} \right)} = {\left( \frac{K_{i\; 1}s}{s^{2} + \left( \omega_{o} \right)^{2}} \right){err}_{{pj}\; 2}}},{and}$${R_{2}\left( {err}_{{pj}\; 2} \right)} = {\left( \frac{K_{i\; 2}s}{s^{2} + \left( {2\omega_{o}} \right)^{2}} \right){{err}_{{pj}\; 2}.}}$

Here, K_(p), K_(i1), and K_(i2) may denote predetermined gain values,and ω_(o) denotes a AC-grid frequency.

In yet another further exemplary embodiment, the inputting of thecurrent reference value (i*_(pj2)) of the upper valve of the modularmulti-level converter may include calculating the current referencevalue (i*_(pj2)) using the following equation:

${i_{{pj}\; 2}^{*} = {\frac{i_{{dc}\; 2}^{*}}{3} + {\frac{i_{sj}^{*}}{2}\mspace{14mu} \left( {{j = a},b,c} \right)}}},$

and i*_(dc2) may denote a DC current reference value flowing in a DCsystem and i*_(sj) may denote a reference value regarding a phasecurrent.

In still yet another further exemplary embodiment, the reference valueregarding the phase current may be calculated into an expression of astationary reference frame using the following equation:

$\begin{bmatrix}i_{sa}^{*} \\i_{sb}^{*} \\i_{sc}^{*}\end{bmatrix} = {{\begin{bmatrix}1 & 0 \\{- \frac{1}{2}} & \frac{\sqrt{3}}{2} \\{- \frac{1}{2}} & {- \frac{\sqrt{3}}{2}}\end{bmatrix}\begin{bmatrix}i_{s\; \alpha}^{*} \\i_{s\; \beta}^{*}\end{bmatrix}}.}$

Here, i*_(sα) and i*_(sβ) may denote the reference value regarding thephase current expressed into a rotating stationary reference frame.

In a still further exemplary embodiment, i*_(sα) and i*_(sβ) may convertan expression of the reference value regarding the phase current at ad-q frame into the rotating stationary reference frame using thefollowing equation:

i* _(sαβ) =i _(sdq) ^(p*) e ^(jωt) +i _(sdq) ^(n*) e ^(−jωt)

Here, i_(sdq) ^(p*) may be an abbreviation of a d-axis and a q-axis(i_(sq) ^(p*),i_(sd) ^(p*)) of a positive sequence component currentreference value; i_(sdq) ^(n*) may be an abbreviation of a d-axis and aq-axis (i_(sq) ^(n*),i_(sd) ^(n*)) of a negative sequence componentcurrent reference value; i_(sd) ^(p*) may denote the d-axis of thepositive sequence component current reference value; i_(sq) ^(p*) maydenote the q-axis of the positive sequence component current referencevalue; i_(sd) ^(n*) may denote the d-axis of the negative sequencecomponent current reference value; i_(sq) ^(n*) may denote the q-axis ofthe negative sequence component current reference value; i_(sq) ^(p*),i_(sd) ^(p*), i_(sq) ^(n*), and i_(sd) ^(n*) may be calculated using thefollowing equations:

${i_{sq}^{p^{*}} = {{PI}\left( {P_{s}^{*} - P_{s}} \right)}},{i_{sd}^{p^{*}} = {{PI}\left( {Q_{s}^{*} - Q_{s}} \right)}},{i_{sq}^{n^{*}} = {{{- \frac{E_{sd}^{n}}{E_{sq}^{p}}}i_{sd}^{p}} - {\frac{E_{sq}^{n}}{E_{sq}^{p}}i_{sq}^{p}}}},{and}$$i_{sd}^{n^{*}} = {{\frac{E_{sq}^{n}}{E_{sq}^{p}}i_{sd}^{p}} - {\frac{E_{sd}^{n}}{E_{sq}^{p}}{i_{sq}^{p}.}}}$

Here, P_(s) may denote active power in the AC system, P*_(s) may denotea reference value of active power in the AC system, Q_(s) may denotereactive power in the AC system, Q*_(s) may denote a reference value ofreactive power in the AC system, E_(sd) ^(p) may denote a d-axis voltageof a positive sequence voltage flowing in the AC system, E_(sq) ^(p) maydenote a q-axis voltage of a positive sequence voltage flowing in the ACsystem, E_(sd) ^(n) may denote a d-axis voltage of a negative sequencevoltage flowing in the AC system, and E_(sq) ^(n) may denote a q-axisvoltage of a negative sequence voltage flowing in the AC system.

In a yet still further exemplary embodiment, the reference value(i*_(dc2)) of the DC system may be calculated using the followingequation:

$i_{{dc}\; 2}^{*} = {\frac{3}{2}\left( \frac{E_{sq}^{p}}{V_{{dc}\; 2}} \right){i_{sq}^{p^{*}}.}}$

Here, E_(sq) ^(p) may denote a q-axis voltage of a positive sequencecomponent voltage flowing in the AC system and i_(sq) ^(p*) may denote aq-axis current of a positive sequence component current reference valueflowing in the AC system.

In a yet still further exemplary embodiment, after the calculating ofthe voltage reference value (u*_(pj2)) using the current reference value(i*_(pj2)), the measured current value (i_(pj2)), the error value(err_(pj2)), the DC link voltage value (V_(dc2)), and the AC-gridvoltage value (E_(sj)), the driving method may include: calculating thenumber of submodules to be triggered among submodules of the uppervalve; selecting submodules corresponding to the number of submodules;and applying a pulse width modulation signal to the selected submodules.

In another aspect, the present invention provides a driving method for amodular multi-level converter that converts an alternating current (AC)into a direct current (DC) or converts a DC into an AC using the modularmulti-level converter with a plurality of submodules stacked to deliverpower in an AC system, the modular multi-level converter comprising aplurality of valves independently driven and a lower valve that is oneof valve branches comprising the valves, the method comprising:inputting a current reference value (i*_(nj2)) of the lower valve of themodular multi-level converter; measuring a current value (i_(nj2)) ofthe valve; calculating an error value (err_(nj2)) between the currentreference value and the measured current value of the lower valve;measuring a DC link voltage value (V_(dc2)) of the modular multi-levelconverter; measuring a system voltage value (E_(sj)) of the modularmulti-level converter; and calculating a voltage reference value(u*_(pj2)) using the current reference value (i*_(nj2)) the measuredcurrent value (i_(nj2)), the error value (err_(nj2)), the DC linkvoltage value (V_(dc2)), and the AC-grid voltage value (E_(sj)).

In an exemplary embodiment, the driving method may further includecalculating a parameter variation value ({circumflex over (l)}_(nj2)) ofa circulating current suppression inductor of the modular multi-levelconverter between the measuring of the AC-grid voltage value (E_(sj)) ofthe modular multi-level converter and calculating of the voltagereference value (u*_(nj2)) using the current reference value, themeasured current value, the error value, the DC link voltage value, andthe system voltage value.

In another exemplary embodiment, the calculating of the parametervariation value ({circumflex over (l)}_(nj2)) of a circulating currentsuppression inductor of the modular multi-level converter may include:obtaining a differential value of the parameter variation value of thecirculating current suppression inductor using the following equation:

{circumflex over (l)}_(nj2)−m₂err_(nj2); and integrating thedifferential value of the parameter variation value of the circulatingcurrent suppression inductor. Here, m₂ may be a predetermined tuningconstant.

In still another exemplary embodiment, the calculating of the voltagereference value (u*_(nj2)) using the current reference value (i*_(nj2))the measured current value (i_(nj2)), the error value (err_(nj2)), theDC link voltage value (V_(dc2)), the AC-grid voltage value (E_(sj)), andthe parameter variation value ({circumflex over (l)}_(nj2)) of theinductor may include calculating the voltage reference value (u*_(nj2))using the following equation:

$u_{{nj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} + E_{sj}} \right) - \left\{ {{P\left( {err}_{{nj}\; 2} \right)} + {R_{1}\left( {err}_{{nj}\; 2} \right)} + {R_{2}\left( {err}_{{nj}\; 2} \right)}} \right\} + {\left\{ {L_{s}{\hat{l}}_{{nj}\; 2}} \right\}.}}$

In yet another exemplary embodiment, the calculating of the voltagereference value (u*_(nj2)) using the current reference value (i*_(nj2)),the measured current value (i_(nj2)), the error value (err_(nj2)), theDC link voltage value (V_(dc2)), the AC-grid voltage value (E_(sj)), andthe parameter variation value ({circumflex over (l)}_(nj2)) of theinductor may include calculating the voltage reference value (u*_(nj2))using the following equation:

$u_{{nj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} + E_{sj}} \right) - \left\{ {{P\left( {err}_{{nj}\; 2} \right)} + {R_{1}\left( {err}_{{nj}\; 2} \right)} + {R_{2}\left( {err}_{{nj}\; 2} \right)}} \right\} - {\left\{ {{L_{s}i_{{nj}\; 2}^{*}} - {L_{s}{\hat{l}}_{{nj}\; 2}}} \right\}.}}$

In still yet another exemplary embodiment, the calculating of thevoltage reference value (u*_(nj2)) using the current reference value(i*_(nj2)), the measured current value (i_(nj2)), the error value(err_(nj2)), the DC link voltage value (V_(dc2)), and the AC-gridvoltage value (E_(sj)) may include calculating the voltage referencevalue (u*_(nj2)) using the following equation:

$u_{{nj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} + E_{sj}} \right) - {\left\{ {{P\left( {err}_{{nj}\; 2} \right)} + {R_{1}\left( {err}_{{nj}\; 2} \right)} + {R_{2}\left( {err}_{{nj}\; 2} \right)}} \right\}.}}$

In a further exemplary embodiment, the calculating of the voltagereference value (u*_(nj2)) using the current reference value (i*_(nj2)),the measured current value (i_(nj2)), the error value (err_(nj2)), theDC link voltage value (V_(dc2)), the AC-grid voltage value (E_(sj)), andan sgn function may include calculating the voltage reference value(u*_(nj2)) using the following equation:

$u_{{nj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} + E_{sj}} \right) - \left\{ {{P\left( {err}_{{nj}\; 2} \right)} + {R_{1}\left( {err}_{{nj}\; 2} \right)} + {R_{2}\left( {err}_{{nj}\; 2} \right)}} \right\} - {\left\{ {\rho_{{nj}\; 2}{{sgn}\left( {err}_{{nj}\; 2} \right)}} \right\}.}}$

Here, the sign function may denote a sign function operated by thefollowing equations:

sgn(err _(nj2))=1(err _(nj2)>0)

sgn(err _(nj2))=0(err _(nj2)≦0)

and ρ_(pj2) may denote a proportional gain.

In another further exemplary embodiment, the calculating of the voltagereference value (u*_(nj2)) using the current reference value (i*_(nj2)),the measured current value (i_(nj2)), the error value (err_(nj2)), theDC link voltage value (V_(dc2)), the AC-grid voltage value (E_(sj)), andan sgn function may include calculating the voltage reference value(u*_(nj2)) using the following equation:

${u_{{nj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} + E_{sj}} \right) - \left\{ {{P\left( {err}_{{nj}\; 2} \right)} + {R_{1}\left( {err}_{{nj}\; 2} \right)} + {R_{2}\left( {err}_{{nj}\; 2} \right)}} \right\} - \left\{ {{L_{s}{\overset{\prime}{i}}_{{nj}\; 2}^{*}} + {\rho_{{nj}\; 2}{{sgn}\left( {err}_{{nj}\; 2} \right)}}} \right\}}},$

Here, the sign function denotes a sign function operated by thefollowing equations:

sgn(err _(nj2))=1(err _(nj2)>0)

sgn(err _(nj2))=0(err _(nj2)≦0)

ρ_(nj2) may denote a proportional gain; and L_(s) may denote acirculating current suppression inductor of the upper valve.

In still another further exemplary embodiment, P(err_(nj2)),R₁(err_(nj2)), and R₂(err_(nj2)) may be calculated using the followingequations:

${{P\left( {err}_{{nj}\; 2} \right)} = {\left( K_{p} \right){err}_{{nj}\; 2}}},{{R_{1}\left( {err}_{{nj}\; 2} \right)} = {\left( \frac{K_{i\; 1}s}{s^{2} + \left( \omega_{o} \right)^{2}} \right){err}_{{nj}\; 2}}},{and}$${R_{2}\left( {err}_{{nj}\; 2} \right)} = {\left( \frac{K_{i\; 2}s}{s^{2} + \left( {2\omega_{o}} \right)^{2}} \right){{err}_{{nj}\; 2}.}}$

Here, K_(p), K_(i1), and K_(i2) may denote predetermined gain values,and ω_(o) may denote a AC-grid frequency.

In yet another further exemplary embodiment, the inputting of thecurrent reference value (i*_(nj2)) of the upper valve of the modularmulti-level converter may include calculating the current referencevalue (i*_(nj2)) using the following equation:

$i_{{nj}\; 2}^{*} = {\frac{i_{{dc}\; 2}^{*}}{3} - {\frac{i_{sj}^{*}}{2}.}}$

Here, i*_(dc2) may denote a DC current reference value flowing in a DCsystem and i*_(sj) may denote a reference value regarding a phasecurrent.

In still yet another further exemplary embodiment, the reference valueregarding the phase current may be calculated into an expression of astationary reference frame using the following equation:

${\begin{bmatrix}i_{sa}^{*} \\i_{sb}^{*} \\i_{sc}^{*}\end{bmatrix} = {\begin{bmatrix}1 & 0 \\{- \frac{1}{2}} & \frac{\sqrt{3}}{2} \\{- \frac{1}{2}} & {- \frac{\sqrt{3}}{2}}\end{bmatrix}\begin{bmatrix}i_{s\; \alpha}^{*} \\i_{s\; \beta}^{*}\end{bmatrix}}},$

and i*_(sα) and i*_(sβ) may denote the reference value regarding thephase current expressed into a rotating stationary reference frame.

In a still further exemplary embodiment, i*_(sα) and i*_(sβ) may convertan expression of the reference value regarding the phase current at ad-q frame into the rotating stationary reference frame using thefollowing equation:

i* _(sαβ) =i _(sdq) ^(p*) e ^(jωt) i _(sdq) ^(n*) e ^(−jωt);

i_(sdq) ^(p*) may be an abbreviation of a d-axis and a q-axis (i_(sq)^(p*),i_(sd) ^(p*)) of a positive sequence component current referencevalue; i_(sdq) ^(n*) may be an abbreviation of a d-axis and a q-axis(i_(sq) ^(n*),i_(sd) ^(n*)) of a negative sequence component currentreference value; i_(sd) ^(p*) may denote the d-axis of the positivesequence component current reference value; i_(sq) ^(p*) may denote theq-axis of the positive sequence component current reference value;i_(sd) ^(n*) may denote the d-axis of the negative sequence componentcurrent reference value; i_(sq) ^(n*) may denote the q-axis of thenegative sequence component current reference value; i_(sq) ^(p*),i_(sd) ^(p*), i_(sq) ^(n*), and i_(sd) ^(n*) may be calculated using thefollowing equations:

${i_{sq}^{p*} = {{PI}\left( {P_{s}^{*} - P_{s}} \right)}},{i_{sd}^{p*} = {{PI}\left( {Q_{s}^{*} - Q_{s}} \right)}},{i_{sq}^{n*} = {{{- \frac{E_{sd}^{n}}{E_{sq}^{p}}}i_{sd}^{p}} - {\frac{E_{sq}^{n}}{E_{sq}^{p}}i_{sq}^{p}}}},{and}$$i_{sd}^{n*} = {{\frac{E_{sq}^{n}}{E_{sq}^{p}}i_{sd}^{p}} - {\frac{E_{sd}^{n}}{E_{sq}^{p}}{i_{sq}^{p}.}}}$

Here, P_(s) may denote active power in the AC system, P*_(s) may denotea reference value of active power in the AC system, Q_(s) may denotereactive power in the AC system, Q*_(s) may denote a reference value ofreactive power in the AC system, E_(sd) ^(p) may denote a d-axis voltageof a positive sequence voltage flowing in the AC system, E_(sq) ^(p) maydenote a q-axis voltage of a positive sequence voltage flowing in the ACsystem, E_(sd) ^(n) may denote a d-axis voltage of a negative sequencevoltage flowing in the AC system, and E_(sq) ^(n) may denote a q-axisvoltage of a negative sequence voltage flowing in the AC system.

In a yet still further exemplary embodiment, the reference value(i*_(dc2)) of the DC system may be calculated using the followingequation:

${i_{{dc}\; 2}^{*} = {\frac{3}{2}\left( \frac{E_{sq}^{p}}{V_{{dc}\; 2}} \right)i_{sq}^{p*}}},$

and

Here, E_(sq) ^(p) may denote a q-axis voltage of a positive sequencecomponent voltage flowing in the AC system and i_(sq) ^(p*) may denote aq-axis current of a positive sequence component current reference valueflowing in the AC system.

In a yet still further exemplary embodiment, after the calculating ofthe voltage reference value (u*_(pj2)) using the current reference value(i*_(pj2)), the measured current value (i_(pj2)), the error value(err_(pj2)), the DC link voltage value (V_(dc2)), and the AC-gridvoltage value (E_(sj)), the driving method may include: calculating thenumber of submodules to be triggered among submodules of the uppervalve; selecting submodules corresponding to the number of submodules;and applying a pulse width modulation signal to the selected submodules.

In a yet still further exemplary embodiment, the driving method for themodular multi-level converter may be driven at a valve unit of themodular multi-level converter.

In still another aspect, the present invention provides a drivingapparatus for a modular multi-level converter, including: an input unitreceiving a current reference value of an upper valve of one valvebranch of the modular multi-level converter; a current measuring unitfor measuring a current value of the upper valve of the modularmulti-level converter; a direct current (DC) link voltage measuring unitfor measuring a voltage value of a DC link of the modular multi-levelconverter; a system voltage measuring unit for measuring a systemvoltage value of the modular multi-level converter; an error calculatingunit for calculating an error value between the current reference valuereceived by the input unit and the current value measured by the currentmeasuring unit; a proportional controller proportionally amplifying theerror value calculated by the error calculating unit; a firstresonant-type current controller receiving the error value calculated bythe error calculating unit to converge an error current equal to aAC-grid frequency to zero; a second resonant-type current controllerreceiving the error value calculated by the error calculating unit toconverge a harmonic error current about two times larger than theAC-grid frequency to zero; and a voltage reference value calculatingunit for calculating a voltage reference value of the upper valve of theone valve branch of the modular multi-level converter using the valuescalculated by the DC link voltage measuring unit, the system voltagemeasuring unit, the proportional controller, the first resonant-typecurrent controller, and the second resonant-type current controller.

In an exemplary embodiment, the driving apparatus may further include: asubmodule selecting unit for selecting the number of submodules to betriggered and the submodules to be triggered, using the voltagereference value calculated by the voltage reference value calculatingunit; and a pulse width modulation signal generating unit applying apulse width modulation signal to the submodules selected by thesubmodule selecting unit.

In another exemplary embodiment, the proportional controller may amplifythe error value calculated by the error calculating unit to a gainvalue.

In still another exemplary embodiment, the first resonant-type currentcontroller may multiply the error value calculated by the errorcalculating unit and the following equation:

$\frac{K_{i\; 1}s}{s^{2} + \left( \omega_{o} \right)^{2}}$

to converge the error current to zero.

Here, K_(i1) denotes a predetermined gain value of the firstresonant-type current controller and ω_(o) may denote the AC-gridfrequency.

In yet another exemplary embodiment, the second resonant-type currentcontroller may multiply the error value calculated by the errorcalculating unit and the following equation:

$\frac{K_{i\; 2}s}{s^{2} + \left( {2\; \omega_{o}} \right)^{2}}$

to converge the harmonic error current about two times larger than theAC-grid frequency to zero.

Here, K_(i2) may denote a predetermined gain value of the secondresonant-type current controller and ω_(o) may denote the AC-gridfrequency.

In still yet another exemplary embodiment, the voltage reference valuecalculating unit may obtain a voltage difference by subtracting theAC-grid voltage value measured by the system voltage measuring unit froma half of the voltage value measured by the DC link voltage measuringunit, and may calculate the voltage reference value by subtracting a sumof the calculated values outputted by the proportional controller, thefirst resonant-type current controller, and the second resonant-typecurrent controller from the voltage difference.

In a further exemplary embodiment, the driving apparatus may furtherinclude a compensator reducing an error generated from the modularmulti-level converter. Here, the compensator may obtain an sgn outputvalue by inputting the error value of the error calculating unit into ansgn function and then calculate a compensation value by multiplying thesgn output value and a proportional gain of the sgn function, and thesgn function is a sign function.

In another further exemplary embodiment, the voltage reference valuecalculating unit further may receive an output value of the compensatorto obtain a voltage difference by subtracting the AC-grid voltage valuemeasured by the system voltage measuring unit from a half of the voltagevalue measured by the DC link voltage measuring unit, and calculate thevoltage reference value by subtracting a sum of the calculated valuesoutputted by the proportional controller, the first resonant-typecurrent controller, the second resonant-type current controller, and thecompensator from the voltage difference.

In still another further exemplary embodiment, the driving apparatus mayfurther include an estimator that obtains a variation estimation valueby multiplying and integrating the error value calculated by the errorcalculating unit and a predetermined tuning constant to remove dynamiccharacteristics due to a variation of circulating current suppressioninductor and resistor components of the modular multi-level converter.

In yet another further exemplary embodiment, the voltage reference valuecalculating unit may further receive an estimation value of theestimator to obtain a voltage difference by subtracting the AC-gridvoltage value measured by the system voltage measuring unit from a halfof the voltage value measured by the DC link voltage measuring unit, andcalculate the voltage reference value by subtracting a sum of thecalculated values outputted by the proportional controller, the firstresonant-type current controller, the second resonant-type currentcontroller, the compensator, and the estimator from the voltagedifference.

In a further aspect, the present invention provides a driving apparatusfor a modular multi-level converter, including: an input unit receivinga current reference value of a lower valve of one valve branch of themodular multi-level converter; a current measuring unit for measuring acurrent value of the lower valve of the modular multi-level converter; adirect current (DC) link voltage measuring unit for measuring a voltagevalue of a DC link of the modular multi-level converter; a systemvoltage measuring unit for measuring a system voltage value of themodular multi-level converter; an error calculating unit for calculatingan error value between the current reference value received by the inputunit and the current value measured by the current measuring unit; aproportional controller proportionally amplifying the error valuecalculated by the error calculating unit; a first resonant-type currentcontroller receiving the error value calculated by the error calculatingunit to converge an error current equal to a AC-grid frequency to zero;a second resonant-type current controller receiving the error valuecalculated by the error calculating unit to converge a harmonic errorcurrent about two times larger than the AC-grid frequency to zero; and avoltage reference value calculating unit for calculating a voltagereference value of the lower valve of the one valve branch of themodular multi-level converter using the values calculated by the DC linkvoltage measuring unit, the system voltage measuring unit, theproportional controller, the first resonant-type current controller, andthe second resonant-type current controller.

In an exemplary embodiment, the driving apparatus may further include: asubmodule selecting unit for selecting the number of submodules to betriggered and the submodules to be triggered, using the voltagereference value calculated by the voltage reference value calculatingunit; and a pulse width modulation signal generating unit applying apulse width modulation signal to the submodules selected by thesubmodule selecting unit.

In another exemplary embodiment, the proportional controller may amplifythe error value calculated by the error calculating unit to a gainvalue.

In still another exemplary embodiment, the first resonant-type currentcontroller may multiply the error value calculated by the errorcalculating unit and the following equation:

$\frac{K_{i\; 1}s}{s^{2} + \left( \omega_{o} \right)^{2}}$

to converge the error current to zero.

Here, K_(i1) may denote a predetermined gain value of the firstresonant-type current controller and ω_(o) denotes the AC-gridfrequency.

The driving apparatus of claim 40, wherein the second resonant-typecurrent controller may multiply the error value calculated by the errorcalculating unit and the following equation:

$\frac{K_{i\; 2}s}{s^{2} + \left( {2\; \omega_{o}} \right)^{2}}$

to converge the harmonic error current about two times larger than theAC-grid frequency to zero.

Here, K_(i2) may denote a predetermined gain value of the secondresonant-type current controller and ω_(o) may denote the AC-gridfrequency.

In yet another exemplary embodiment, the voltage reference valuecalculating unit may obtain a voltage sum by adding the AC-grid voltagevalue measured by the system voltage measuring unit to a half of thevoltage value measured by the DC link voltage measuring unit, andcalculate the voltage reference value by subtracting a sum of thecalculated values outputted by the proportional controller, the firstresonant-type current controller, and the second resonant-type currentcontroller from the voltage sum.

In still yet another exemplary embodiment, the driving apparatus mayfurther include a compensator reducing an error generated from themodular multi-level converter. Here, the compensator may obtain an sgnoutput value by inputting the error value of the error calculating unitinto an sgn function and then calculate a compensation value bymultiplying the sgn output value and a proportional gain of the sgnfunction, and the sgn function may be a sign function.

In a further exemplary embodiment, the voltage reference valuecalculating unit may further receive an output value of the compensatorto obtain a voltage sum by adding the AC-grid voltage value measured bythe system voltage measuring unit to a half of the voltage valuemeasured by the DC link voltage measuring unit, and calculate thevoltage reference value by subtracting a sum of the calculated valuesoutputted by the proportional controller, the first resonant-typecurrent controller, the second resonant-type current controller, and thecompensator from the voltage sum.

In another further exemplary embodiment, the driving apparatus mayfurther include an estimator that obtains a variation estimation valueby multiplying and integrating the error value calculated by the errorcalculating unit and a predetermined constant to remove dynamiccharacteristics due to a variation of circulating current suppressioninductor and resistor components of the modular multi-level converter.

In still another further exemplary embodiment, the voltage referencevalue calculating unit may further receive an estimation value of theestimator to obtain a voltage sum by adding the AC-grid voltage valuemeasured by the system voltage measuring unit to a half of the voltagevalue measured by the DC link voltage measuring unit, and calculate thevoltage reference value by subtracting a sum of the calculated valuesoutputted by the proportional controller, the first resonant-typecurrent controller, the second resonant-type current controller, thecompensator, and the estimator from the voltage sum.

In yet another further exemplary embodiment, the driving apparatus forthe modular multi-level converter may be driven at a valve unit of themodular multi-level converter.

Other aspects and exemplary embodiments of the invention are discussedinfra.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other features of the present invention will now bedescribed in detail with reference to certain exemplary embodimentsthereof illustrated the accompanying drawings which are givenhereinbelow by way of illustration only, and thus are not limitative ofthe present invention, and wherein:

FIG. 1 is a view illustrating a configuration of a High VoltageDirect-Current (HVDC) transmission system to which a driving method of amodular multi-level converter is applied according to an exemplaryembodiment of the present invention;

FIG. 2 is a view illustrating one of multi-level converters to which adriving method of a modular multi-level converter is applied accordingto an exemplary embodiment of the present invention, where themulti-level converters at both ends are bilaterally symmetricallydisposed across a high voltage DC line;

FIG. 3 is a view illustrating types of submodules that can be applied toa driving apparatus and method for a modular multi-level converteraccording to an exemplary embodiment of the present invention;

FIG. 4 is a view illustrating an equivalent circuit with respect to avalve branch taking charge of one phase in a multi-level converter towhich a driving method for a modular multi-level converter is appliedaccording to an exemplary embodiment of the present invention;

FIG. 5 is a view illustrating an internal configuration of a drivingapparatus and method for a modular multi-level converter according to anexemplary embodiment of the present invention, where three upper valvesare controlled;

FIG. 6 is a view illustrating an internal configuration of a drivingapparatus and method for a modular multi-level converter according to anexemplary embodiment of the present invention, where three lower valvesare controlled;

FIG. 7 is a view illustrating a simplified example of the drivingapparatus for the modular multi-level converter of FIG. 5;

FIG. 8 is a view illustrating a simplified example of the drivingapparatus for the modular multi-level converter of FIG. 6;

FIG. 9 is a view illustrating an estimator added to the drivingapparatus for the modular multi-level converter of FIG. 7;

FIG. 10 is a view illustrating an estimator added to the drivingapparatus for the modular multi-level converter of FIG. 8;

FIG. 11 is a view illustrating a relationship between a drivingapparatus for a modular multi-level converter and an upper controllerthereover according to an exemplary embodiment of the present invention;

FIG. 12 is a view illustrating a pulse width modulation signal appliedto a driving apparatus for a modular multi-level converter according toan exemplary embodiment of the present invention;

FIG. 13 is a graph illustrating values measured in each system and DClink when a circulating current is not suppressed in a typicalmulti-level converter;

FIG. 14 is a graph illustrating results of control using the method ofQingrui Tu (2012) when an unbalance state occurs in a typicalmulti-level converter;

FIG. 15 is a view illustrating a configuration of a modular multi-levelconverter using a driving method of the modular multi-level converteraccording to an exemplary embodiment of the present invention;

FIG. 16 is a view illustrating values of parameters to be used in adriving apparatus and method for a modular multi-level converteraccording to an exemplary embodiment of the present invention;

FIG. 17 is a graph illustrating results of control by a drivingapparatus and method for a modular multi-level converter according to anexemplary embodiment of the present invention;

FIG. 18 is a view illustrating a valve current and a reference value ofthe valve current of the driving apparatus and method for the modularmulti-level converter of FIG. 17;

FIG. 19 is a view illustrating another example of typical circulatingcurrent suppression methods, proposed by Antonious Anotonopoulos andMaryam Saeedifard, where a region marked by a box shows a methodproposed by Antonious Anotonopoulos and the other region shows a methodproposed by Maryam Saeedifard;

FIG. 20 is a view illustrating one of typical circulating currentsuppression methods, proposed by Qingrui Tu; and

FIG. 21 is a view illustrating a control device for implementing avariety of typical methods described above.

Reference numerals set forth in the Drawings includes reference to thefollowing elements as further discussed below:

-   -   1: upper controller    -   2: valve controller    -   10: submodule    -   20: driving apparatus for modular multi-level converter    -   21: proportional controller    -   22: first resonant-type current controller    -   23: second resonant-type current controller    -   24: compensator    -   25: estimator    -   30: upper controller    -   100: upper valve    -   200: lower valve

It should be understood that the accompanying drawings are notnecessarily to scale, presenting a somewhat simplified representation ofvarious exemplary features illustrative of the basic principles of theinvention. The specific design features of the present invention asdisclosed herein, including, for example, specific dimensions,orientations, locations, and shapes will be determined in part by theparticular intended application and use environment.

In the figures, reference numbers refer to the same or equivalent partsof the present invention throughout the several figures of the drawing.

DETAILED DESCRIPTION

Hereinafter reference will now be made in detail to various embodimentsof the present invention, examples of which are illustrated in theaccompanying drawings and described below. While the invention will bedescribed in conjunction with exemplary embodiments, it will beunderstood that present description is not intended to limit theinvention to those exemplary embodiments. On the contrary, the inventionis intended to cover not only the exemplary embodiments, but alsovarious alternatives, modifications, equivalents and other embodiments,which may be included within the spirit and scope of the invention asdefined by the appended claims.

The above and other features of the invention are discussed infra.

Hereinafter, exemplary embodiments of the present invention will bedescribed in detail with reference to the accompanying drawings so thatthose skilled in the art can easily carry out the present invention.

FIG. 1 is a view illustrating a configuration of a High VoltageDirect-Current (HVDC) transmission system to which a driving method of amodular multi-level converter is applied according to an exemplaryembodiment of the present invention.

An HVDC system with a modular multi-level converter may includemulti-level converters MMC_1 and MMC_2 at both ends thereof across ahigh voltage direct current (DC) line. The multi-level converter mayhave a structure that is connected to a 3-phase alternating current (AC)system.

Also, each phase may include an upper valve 100 and a lower valve 200,and may include an upper valve controller for controlling the uppervalve 100 and a lower valve controller for controlling the lower valve200.

FIG. 2 is a view illustrating one of multi-level converters to which adriving method of a modular multi-level converter is applied accordingto an exemplary embodiment of the present invention, where themulti-level converters at both ends are bilaterally symmetricallydisposed across a high voltage DC line.

FIG. 3 is a view illustrating types of submodules 10 that can be appliedto a driving apparatus and method for a modular multi-level converteraccording to an exemplary embodiment of the present invention.

FIG. 3A shows a half bridge type submodule, and FIG. 3B shows a fullbridge type submodule. Also, FIG. 3C shows a clamp double typesubmodule.

Submodules of a driving apparatus for a modular multi-level converteraccording to an exemplary embodiment of the present invention mayinclude the above-mentioned submodules, but the present invention is notlimited thereto. Accordingly, it can be easily understood by thoseskilled in the art that various types of submodules can be used as thesubmodules.

First, in order to described an operational process of a drivingapparatus and method for a modular multi-level converter according to anexemplary embodiment of the present invention, a voltage equation of avalve branch at one side of the modular multi-level converter will bededuced.

FIG. 4 is a view illustrating an equivalent circuit with respect to avalve branch taking charge of one phase in a multi-level converter towhich a driving method for a modular multi-level converter is appliedaccording to an exemplary embodiment of the present invention. Here, thevalve branch refers to all upper and lower valves of the modularmulti-level converter which take charge of one phase.

When a capacitor voltage at the upper valve of the multi-level converteris v_(cpj) (j=a,b,c), a capacitor voltage at the lower valve of themulti-level converter is v_(cnj) (j=a,b,c), a circulating currentsuppression inductor is L_(s), and a resistance of an inductor and acable is R_(s), an equivalent circuit of one phase of the modularmulti-level converter of FIGS. 1 and 2 can be represented like FIG. 4.

From two closed loops in which an upper valve current (i_(pj2): j=a,b,c)and a lower valve current (i_(nj2)) flow, a voltage equation of theupper valve (v_(pj):j=a,b,c) and a voltage equation of the lower valve(v_(nj)) can be expressed as Equations (1) and (2) below.

$\begin{matrix}{{u_{{pj}\; 2} + {R_{s}i_{{pj}\; 2}} + {L_{s}\frac{i_{{pj}\; 2}}{t}} + E_{sj} - \frac{V_{{dc}\; 2}}{2}} = 0} & (1) \\{{u_{{nj}\; 2} + {R_{s}i_{{nj}\; 2}} + {L_{s}\frac{i_{{nj}\; 2}}{t}} - \frac{V_{{dc}\; 2}}{2} - E_{sj}} = 0} & (2)\end{matrix}$

Here, the first term of Equation (1) may represent the sum (u_(pj2)) ofthe capacitor voltages of the upper valve, and the first term ofEquation (2) may represent the sum (u_(nj2)) of the capacitor voltagesof the lower valve. In Equations (1) and (2), R_(s) may representresistance values (not shown) of the upper valve and the lower valve ofthe modular multi-level converter.

$\begin{matrix}{u_{{pj}\; 2}\overset{\Delta}{=}{\sum\limits_{i = 1}^{N_{{pj}\; 2}}\; \left( v_{Cpji} \right)}} & (3) \\{u_{{nj}\; 2}\overset{\Delta}{=}{\sum\limits_{i = 1}^{N_{{nj}\; 2}}\; \left( v_{Cnji} \right)}} & (4)\end{matrix}$

If Equations (1) and (2) are transformed into a state equation withrespect to the upper valve current (i_(pj2)) and the lower valve current(i_(nj2)), Equations (5) and (6) can be obtained.

$\begin{matrix}{\frac{i_{{pj}\; 2}}{t} = {{{- \frac{R_{s}}{L_{s}}}i_{{pj}\; 2}} + {\frac{1}{L_{s}}\left\{ {\frac{V_{{dc}\; 2}}{2} - u_{{pj}\; 2}} \right\}} - {\frac{1}{L_{s}}E_{sj}}}} & (5) \\{\frac{i_{{nj}\; 2}}{t} = {{{- \frac{R_{s}}{L_{s}}}i_{{nj}\; 2}} + {\frac{1}{L_{s}}\left\{ {\frac{V_{{dc}\; 2}}{2} - u_{{nj}\; 2}} \right\}} + {\frac{1}{L_{s}}{E_{sj}.}}}} & (6)\end{matrix}$

The circulating current suppression inductor L_(s) and resistor R_(s)included in the state equations (5) and (6) may have nominal values,which may be considered to be varied by the manufacturing error and thetemperature within a certain range. All terms related to a parametervariation term may be expressed into a lumped uncertainly term.

Then, when the parameter variation term included in the upper valvecurrent (i_(pj2)) state equation is defined as i_(pj2), and theparameter variation term included in the lower valve current (i_(nj2))state equation is defined as i_(nj2), Equations (5) and (6) may begeneralized as follows.

$\begin{matrix}{\frac{i_{{pj}\; 2}}{t} = {{{- \frac{R_{s}}{L_{s}}}i_{{pj}\; 2}} + {\frac{1}{L_{s}}\left\{ {\frac{V_{{dc}\; 2}}{2} - u_{{pj}\; 2}} \right\}} - {\frac{1}{L_{s}}E_{sj}} + l_{{pj}\; 2}}} & (7) \\{\frac{i_{{nj}\; 2}}{t} = {{{- \frac{R_{s}}{L_{s}}}i_{{nj}\; 2}} + {\frac{1}{L_{s}}\left\{ {\frac{V_{{dc}\; 2}}{2} - u_{{nj}\; 2}} \right\}} + {\frac{1}{L_{s}}E_{sj}} + l_{{nj}\; 2}}} & (8)\end{matrix}$

An error between the reference value (i*_(pj2)) of the upper valvecurrent and the upper valve current (i_(nj2)) may be defined aserr_(pj2), and an error between the reference value (i*_(nj2)) of thelower valve current and the lower valve current (i_(nj2)) may be definedas err_(nj2).

err _(pj2) =i* _(pj2) −i _(pj2)  (9)

err _(nj2) =i* _(nj2) −i _(nj2)  (10)

If Equations (9) and (10) are differentiated and then substituted withEquations (7) and (8), Equations (11) and (12) can be obtained regardinga differential equation with respect to a quintic equation.

$\begin{matrix}{{\overset{.}{err}}_{{pj}\; 2} = {{\overset{\prime}{i}}_{{pj}\; 2}^{*} - \left( {{{- \frac{R_{s}}{L_{s}}}i_{{pj}\; 2}} + {\frac{1}{L_{s}}\left( {\frac{V_{{dc}\; 2}}{2} - u_{{pj}\; 2}} \right)} - {\frac{1}{L_{s}}E_{sj}} + l_{{pj}\; 2}} \right)}} & (11) \\{{\overset{.}{err}}_{{nj}\; 2} = {{\overset{\prime}{i}}_{{nj}\; 2}^{*} - \left( {{{- \frac{R_{s}}{L_{s}}}i_{{nj}\; 2}} + {\frac{1}{L_{s}}\left( {\frac{V_{{dc}\; 2}}{2} - u_{{nj}\; 2}} \right)} + {\frac{1}{L_{s}}E_{sj}} + l_{{nj}\; 2}} \right)}} & (12)\end{matrix}$

In a driving apparatus and method for a modular multi-level converteraccording to an exemplary embodiment of the present invention, a voltagereference value of the upper valve and a voltage reference value of thelower valve that are control inputs may be derived from a state equationusing an upper valve voltage equation and a lower valve voltage equationand a backstepping control method.

The Lyapunov function that is selected to design a controller based onthe backstepping control method may be expressed as Equation (13) below.

V ₁=½err ² _(pj2)+½err ² _(nj2)  (13)

In the driving apparatus and method for the modular multi-levelconverter according to the exemplary embodiment of the presentinvention, when the control input can be determined such that thedifferentiation of the Lyapunov function is smaller than “0”, the uppervalve current (i_(pj2)) may be controlled to be the same as thereference value (i*_(pj2)) of the upper valve current, andsimultaneously the lower valve current (i_(nj2)) may be controlled to bethe same as the reference value (i*_(nj2)) of the lower valve current.

Thus, if the differentiation is performed on the Lyapunov functionexpressed as Equation (13) and then substituted with Equations (11) and(12), Equation (14) can be obtained.

$\begin{matrix}{{\overset{.}{V}}_{1} = {{{err}_{{pj}\; 2}\left\{ {{\overset{\prime}{i}}_{{pj}\; 2}^{*} - \left( {{{- \frac{R_{s}}{L_{s}}}i_{{pj}\; 2}} + {\frac{1}{L_{s}}\left( {\frac{V_{{dc}\; 2}}{2} - u_{{pj}\; 2}} \right)} - {\frac{1}{L_{s}}E_{sj}} + l_{{pj}\; 2}} \right)} \right\}} + {{err}_{{nj}\; 2}\left\{ {{\overset{\prime}{i}}_{{nj}\; 2}^{*} - \left( {{{- \frac{R_{s}}{L_{s}}}i_{{nj}\; 2}} + {\frac{1}{L_{s}}\left( {\frac{V_{{dc}\; 2}}{2} - u_{{nj}\; 2}} \right)} + {\frac{1}{L_{s}}E_{sj}} + l_{{nj}\; 2}} \right)} \right\}}}} & (14)\end{matrix}$

In order to allow Equation (14) that is a differentiation of theLyapunov function to always have a negative value, the upper valvevoltage (u_(pj2)) the lower valve voltage (u_(nj2)) may be selected asEquations (15) and (16) below.

$\begin{matrix}{u_{{pj}\; 2} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - \left\{ {\left( {{K_{{pj}\; 2}{err}_{{pj}\; 2}} + {R_{s}i_{{pj}\; 2}}} \right) + {L_{s}{\overset{\prime}{i}}_{{pj}\; 2}^{*}} - {L_{s}l_{{pj}\; 2}}} \right\}}} & (15) \\{u_{{nj}\; 2} = {\left( {\frac{V_{{dc}\; 2}}{2} + E_{sj}} \right) - {\left\{ {\left( {{K_{{nj}\; 2}{err}_{{nj}\; 2}} + {R_{s}i_{{nj}\; 2}}} \right) + {L_{s}{\overset{\prime}{i}}_{{nj}\; 2}^{*}} - {L_{s}l_{{nj}\; 2}}} \right\}.}}} & (16)\end{matrix}$

However, since a parameter variation term that is an unknown value isincluded in Equations (15) and (16), Equations (15) and (16) cannot bedirectly used to determine a control law. Accordingly, since a parametervariation results in occurrence of an error, the driving apparatus andmethod for the modular multi-level converter according to the exemplaryembodiment of the present invention may include a compensator thatcompensate for the parameter variation in order to inhibit theoccurrence of the error. This compensator can be expressed as Equations(17) and (18) introduced with a sgn function.

L _(s) l _(pj2)=−ρ_(pj2) sgn(err _(pj2))  (17)

L _(s) =l _(nj2)−ρ_(nj2) sgn(err _(nj2))  (18)

Equations (15) and (16) can be rearranged into Equations (19) and (20)using the compensator regarding the parameter variation term.

$\begin{matrix}{u_{{pj}\; 2} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - \left\{ {\left( {{K_{{pj}\; 2}{err}_{{pj}\; 2}} + {R_{s}i_{{pj}\; 2}}} \right) + {L_{s}{\overset{\prime}{i}}_{{pj}\; 2}^{*}} + {\rho_{{pj}\; 2}{{sgn}\left( {err}_{{pj}\; 2} \right)}}} \right\}}} & (19) \\{u_{{nj}\; 2} = {\left( {\frac{V_{{dc}\; 2}}{2} + E_{sj}} \right) - {\left\{ {\left( {{K_{{nj}\; 2}{err}_{{nj}\; 2}} + {R_{s}i_{{nj}\; 2}}} \right) + {L_{s}{\overset{\prime}{i}}_{{nj}\; 2}^{*}} + {\rho_{{nj}\; 2}{{sgn}\left( {err}_{{nj}\; 2} \right)}}} \right\}.}}} & (20)\end{matrix}$

A current corresponding to a half of an AC phase current and a currentcorresponding to a third of a DC current flowing in a DC link voltage,and a circulating current of an AC component flowing between valves maycoexist in the upper valve and the lower valve. The currentcorresponding to the half of the AC phase current may be a componentthat has a AC-grid frequency (ω₀) as a basic frequency, and the ACcomponent of the circulating current may be a component that has afrequency 2 two times larger than the AC-grid frequency.

Accordingly, the driving apparatus and method for the modularmulti-level converter according to the exemplary embodiment of thepresent invention may include a proportional controller 21 and a firstresonant-type current controller 22, which may control active power andreactive power (or DC link voltage control and reactive power) of theAC-grid frequency component (basic frequency) included in the uppervalve current and the lower valve current.

Also, since the frequency component two times larger than the AC-gridfrequency included in the upper valve current and the lower valvecurrent is a component that cannot contribute to the transmission ofenergy, the frequency component needs to be removed. Accordingly, thedriving apparatus and method for the modular multi-level converteraccording to the exemplary embodiment of the present invention mayfurther include a second resonant-type current controller 23 to removethe frequency component.

Thus, the upper valve voltage reference value (u*_(pj2)) and the lowervalve voltage reference value (u*_(nj2)) can be expressed as Equations(21) and (22).

$\begin{matrix}{u_{{pj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - \left\{ {{P\left( {err}_{{pj}\; 2} \right)} + {R_{1}\left( {err}_{{pj}\; 2} \right)} + {R_{2}\left( {err}_{{pj}\; 2} \right)}} \right\} - \left\{ {{L_{s}{\overset{\prime}{i}}_{{pj}\; 2}^{*}} + {\rho_{{pj}\; 2}{{sgn}\left( {err}_{{pj}\; 2} \right)}}} \right\}}} & (21) \\{u_{{nj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} + E_{sj}} \right) - \left\{ {{P\left( {err}_{{nj}\; 2} \right)} + {R_{1}\left( {err}_{{nj}\; 2} \right)} + {R_{2}\left( {err}_{{nj}\; 2} \right)}} \right\} - \left\{ {{L_{s}{\overset{\prime}{i}}_{{nj}\; 2}^{*}} + {\rho_{{nj}\; 2}{sgn}\left( {err}_{{nj}\; 2} \right)}} \right\}}} & (22)\end{matrix}$

Here, P ( ) may indicate the proportional controller 21. Also, R1 ( )may indicate the first resonant-type current controller 22 havingresonance characteristics at the AC-grid frequency, and R2 ( ) mayindicate the second resonant-type current controller 23 having resonancecharacteristics at a frequency two times larger than the AC-gridfrequency so as to remove the circulating current flowing in the upperor lower valve even under the unbalance voltage condition. The last termmay indicate the compensator 24 that can suppress variations of thecirculating current suppression inductor and resistor on the upper orlower valve.

In Equations (21) and (22), the proportional controller 21, the firstresonant-type current controller 22, and the second resonant-typecurrent controller 23 can be expressed as Equations (23) to (25),respectively.

$\begin{matrix}{{P\left( {err}_{{pnj}\; 2} \right)} = {\left( K_{p} \right){err}_{{pnj}\; 2}}} & (23) \\{{R_{1}\left( {err}_{{pnj}\; 2} \right)} = {\left( \frac{K_{i\; 1}s}{s^{2} + \left( \omega_{0} \right)^{2}} \right){err}_{{pnj}\; 2}}} & (24) \\{{R_{2}\left( {err}_{{pnj}\; 2} \right)} = {\left( \frac{K_{i\; 2}s}{s^{2} + \left( {2\omega_{0}} \right)^{2}} \right){err}_{{pnj}_{2}}}} & (25)\end{matrix}$

In Equations (23) to (25), pnj2 may represent either upper valve orlower valve.

Equations (21) and (22) can be expressed as Equations (26) and (27) whencontrollers are designed into a simplified form.

$\begin{matrix}{u_{{pj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - \left\{ {{P\left( {err}_{{pj}\; 2} \right)} + {R_{1}\left( {err}_{{pj}\; 2} \right)} + {R_{2}\left( {err}_{{pj}\; 2} \right)}} \right\} - \left\{ {\rho_{{pj}\; 2}{{sgn}\left( {err}_{{pj}\; 2} \right)}} \right\}}} & (26) \\{u_{{nj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} + E_{sj}} \right) - \left\{ {{P\left( {err}_{{nj}\; 2} \right)} + {R_{1}\left( {err}_{{nj}\; 2} \right)} + {R_{2}\left( {err}_{{nj}\; 2} \right)}} \right\} - \left\{ {\rho_{{nj}\; 2}{{sgn}\left( {err}_{{nj}\; 2} \right)}} \right\}}} & (27)\end{matrix}$

Here, the sgn function denotes a sign function operating with:

sgn(err _(pj2))=1(err _(pj2)>0)

sgn(err _(pj2))=0(err _(pj2)≦0)

sgn(err _(nj2))=1(err _(nj2)>0)

sgn(err _(nj2))=0(err _(nj2)≦0)

and

ρ_(pj2) and ρ_(nj2) denote proportional gains.

The above equation can be further simplified into Equations (28) and(29).

$\begin{matrix}{u_{{pj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - \left\{ {{P\left( {err}_{{pj}\; 2} \right)} + {R_{1}\left( {err}_{{pj}\; 2} \right)} + {R_{2}\left( {err}_{{pj}\; 2} \right)}} \right\}}} & (28) \\{u_{{nj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} + E_{sj}} \right) - \left\{ {{P\left( {err}_{{nj}\; 2} \right)} + {R_{1}\left( {err}_{{nj}\; 2} \right)} + {R_{2}\left( {err}_{{nj}\; 2} \right)}} \right\}}} & (29)\end{matrix}$

Hereinafter, a method of determining the reference value (i*_(pj2)) ofthe upper valve current and the reference value (i*_(nj2)) of the lowervalve current will be described as follows.

A half current of the phase current and the circulating current(i_(diffj)) may mixedly flow in the valve like Equations (30) and (31).

$\begin{matrix}{i_{{pj}\; 2} = {\frac{i_{sj}}{2} + \left( i_{diffj} \right)}} & (30) \\{i_{{nj}\; 2} = {{- \frac{i_{sj}}{2}} + \left( i_{diffj} \right)}} & (31)\end{matrix}$

Since the circulating current can be divided into a DC component and anAC component (i_(dczj)), Equations (30) and (31) can be expressed asEquations (32) and (33) below.

$\begin{matrix}{i_{{pj}\; 2} = {\frac{i_{sj}}{2} + \left( {\frac{i_{{dc}\; 2}}{3} + i_{dczj}} \right)}} & (32) \\{i_{{nj}\; 2} = {{- \frac{i_{sj}}{2}} + \left( {\frac{i_{{dc}\; 2}}{3} + i_{dczj}} \right)}} & (33)\end{matrix}$

In Equations (32) and (33), since the DC component of the circulatingcurrent is a component that is involved in energy transmission, the DCcomponent may not be removed. Accordingly, only the AC component of thecirculating current may be removed.

Thus, the reference value of the valve current can be expressed asEquation (34) using the phase current reference value and the DC linkvoltage other than the AC component of the circulating current havingharmonic characteristics.

$\begin{matrix}{{i_{{pj}\; 2}^{*} = {\frac{i_{{dc}\; 2}^{*}}{3} + \frac{i_{sj}^{*}}{2}}}{i_{{nj}\; 2}^{*} = {\frac{i_{{dc}\; 2}^{*}}{3} - \frac{i_{sj}^{*}}{2}}}\left( {{j = a},b,c} \right)} & (34)\end{matrix}$

Here, the phase current reference value may be determined by Equations(35) to (40).

$\begin{matrix}\begin{matrix}{i_{sq}^{p^{*}} = {{{PI}\left( {V_{{dc}\; 2}^{*} - V_{{dc}\; 2}} \right)}i_{sq}^{p^{*}}}} \\{= {{PI}\left( {P_{s}^{*} - P_{s}} \right)}}\end{matrix} & (35) \\{i_{sd}^{p^{*}} = {{PI}\left( {Q_{s}^{*} - Q_{s}} \right)}} & (36) \\{i_{sq}^{n^{*}} = {{{- \frac{E_{sd}^{n}}{E_{sq}^{p}}}i_{sd}^{p}} - {\frac{E_{sq}^{n}}{E_{sq}^{p}}i_{sq}^{p}}}} & (37) \\{i_{sd}^{n^{*}} = {{\frac{E_{sq}^{n}}{E_{sq}^{p}}i_{sd}^{p}} - {\frac{E_{sd}^{n}}{E_{sq}^{p}}i_{sq}^{p}}}} & (38) \\{i_{s\; {\alpha\beta}}^{*} = {{i_{sdq}^{p^{*}}^{{j\omega}\; t}} + {i_{sdq}^{n^{*}}^{{- {j\omega}}\; t}}}} & (39) \\{\begin{bmatrix}i_{sa}^{*} \\i_{sb}^{*} \\i_{sc}^{*}\end{bmatrix} = {\begin{bmatrix}1 & 0 \\{- \frac{1}{2}} & \frac{\sqrt{3}}{2} \\{- \frac{1}{2}} & {- \frac{\sqrt{3}}{2}}\end{bmatrix}\begin{bmatrix}i_{s\; \alpha}^{*} \\i_{s\; \beta}^{*}\end{bmatrix}}} & (40)\end{matrix}$

That is, regarding the reference value with respect to the phasecurrent, a current reference value may be determined in a d-q frame, andthen is transformed into a stationary reference frame to determine a3-phase current reference value.

A DC current reference value flowing in the DC system may be determinedby the energy conservation law that energy (active power) of the ACsystem and energy (active power) of the DC system are conserved, whichcan be expressed as Equation (41).

$\begin{matrix}{i_{{dc}\; 2}^{*} = {\frac{3}{2}\left( \frac{E_{sq}^{p}}{V_{{dc}\; 2}} \right)i_{sq}^{p^{*}}}} & (41)\end{matrix}$

So far, a method of substituting the parameter variation term(l_(pj2),l_(nj2)) with the sgn( ) function include in Equations (15) and(16) and then designing the control law has been described. From now on,a method of designing the compensator by applying the backsteppingcontrol method with respect to the parameter variation term (l_(pj2),l_(nj2)) will be proposed, and then a method of designing the controllaw using an estimated value ({circumflex over (l)}_(pj2),{circumflexover (l)}_(nj2)) of the parameter variation term will be proposed.

The Lyapunov function that is modified from Equation (13) so as toinclude an error of the estimated value of the parameter variation termcan be expressed as Equation (42).

$\begin{matrix}{V_{1} = {{\frac{1}{2}{err}_{{pj}\; 2}^{2}} + {\frac{1}{2}{err}_{{nj}\; 2}^{2}} + {\frac{1}{2m_{1}}\left( {{\hat{l}}_{{pj}\; 2} - l_{{pj}\; 2}} \right)^{2}} + {\frac{1}{2m_{2}}\left( {{\hat{l}}_{{nj}\; 2} - l_{{nj}\; 2}} \right)^{2}}}} & (42)\end{matrix}$

If Equation (42) is differentiated and then substituted with Equations(11) and (12), Equation (43) in which the estimated value of theparameter variation term is added can be obtained.

$\begin{matrix}{{\overset{.}{V}}_{1} = {{{err}_{{pj}\; 2}\left\{ {{\overset{\prime}{i}}^{*} - \left( {{{- \frac{R_{S}}{L_{s}}}i_{{pj}\; 2}} + {\frac{1}{L_{s}}\left( {\frac{V_{{dc}\; 2}}{2} - u_{{pj}\; 2}} \right)} - {\frac{1}{L_{s}}E_{sj}} + l_{{pj}\; 2}} \right)} \right\}} + {{err}_{{nj}\; 2}\left\{ {{\overset{\prime}{i}}_{{nj}\; 2}^{*} - \left( {{{- \frac{R_{s}}{L_{s}}}i_{{nj}\; 2}} + {\frac{1}{L_{s}}\left( {\frac{V_{{dc}\; 2}}{L_{s}} - u_{{nj}\; 2}} \right)} + {\frac{1}{L_{s}}E_{sj}} + l_{{nj}\; 2}} \right)} \right\}} + {\left( {{\hat{l}}_{{pj}\; 2} - l_{{pj}\; 2}} \right)\frac{{\overset{\prime}{\hat{l}}}_{{pj}\; 2}}{m_{1}}} + {\left( {{\hat{l}}_{{nj}\; 2} - l_{{nj}\; 2}} \right)\frac{{\overset{\prime}{\hat{l}}}_{{pj}\; 2}}{m_{2}}}}} & (43)\end{matrix}$

From the first term and the second term of Equation (43), the uppervalve voltage (u_(pj2)) and the lower valve voltage (u_(nj2)) may beexpressed as Equations (44) and (45), and may be selected in a formincluding the estimated value ({circumflex over (l)}_(pj2),{circumflexover (l)}_(nj2)) of the parameter variation term.

$\begin{matrix}{u_{{pj}\; 2} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - \left\{ {\left( {{L_{s}K_{{pj}\; 2}{err}_{{pj}\; 2}} + {R_{s}i_{{pj}\; 2}}} \right) + {L_{s}{\overset{\prime}{i}}_{{pj}\; 2}^{*}} - {L_{s}{\hat{l}}_{{pj}\; 2}}} \right\}}} & (44) \\{\mspace{79mu} {u_{{nj}\; 2} = {\left( {\frac{V_{{dc}\; 2}}{2} + E_{sj}} \right) - \left\{ {\left( {{L_{s}K_{{nj}\; 2}{err}_{{nj}\; 2}} + {R_{s}i_{{nj}\; 2}}} \right) + {L_{s}{\overset{\prime}{i}}_{{nj}\; 2}^{*}} - {L_{s}{\hat{l}}_{{nj}\; 2}}} \right\}}}} & (45)\end{matrix}$

In order to allow Equation 43 to always have a negative value, ifEquation (43) is substituted with Equations (44) and (45), Equation (43)can be simplified into Equation (46).

$\begin{matrix}{{\overset{\prime}{V}}_{1} = {{{- K_{{pj}\; 2}}{err}_{{pj}\; 2}^{2}} - {K_{{nj}\; 2}{err}_{{nj}\; 2}^{2}} + {\left( {{\hat{l}}_{{pj}\; 2} - l_{{pj}\; 2}} \right)\left( {{err}_{{pj}\; 2} + \frac{{\overset{\overset{\prime}{\hat{}}}{l}}_{{pj}\; 2}}{m_{1}}} \right)} + {\left( {{\hat{l}}_{{nj}\; 2} - l_{{nj}\; 2}} \right){\left( {{err}_{{nj}\; 2} + \frac{{\overset{\overset{\prime}{\hat{}}}{l}}_{{nj}\; 2}}{m_{2}}} \right).}}}} & (46)\end{matrix}$

In order to allow Equation (46) to always have a negative value, thethird term and the fourth term of Equation (46) may be designed to be“0”. A relationship between Equation (47) and Equation (48) may beobtained from the above-mentioned controller design method.

Accordingly, if Equations (47) and (48) are integrated, the estimatedvalues {circumflex over (l)}_(pj2),{circumflex over (l)}_(nj2)) of theparameter variation term can be obtained.

{acute over ({circumflex over (l)}_(pj2) =−m ₁ err _(pj2)  (47)

{acute over ({circumflex over (l)}_(nj2) =−m ₂ err _(nj2)  (48)

Since the estimated values ({circumflex over (l)}_(pj2), {circumflexover (l)}_(nj2)) of the parameter variation term can be seen, thecontrol law that determines the upper valve voltage reference value(u*_(pj2)) and the lower valve voltage reference value (u*_(nj2)) can beobtained.

Similarly to the control law expressed as Equations (21) and (22), thecurrent controller related to control of active power and reactive power(or DC link voltage control and reactive power) having a basic frequency(AC-grid frequency) may be designed with the proportional controller 21and the first resonant-type current controller 22. Also, since allsignals corresponding to two times of the basic frequency (AC-gridfrequency) are harmonic components, the current controller that canremove the harmonic components may be designed with the proportionalcontroller 21 and the second resonant-type current controller 23. Thus,the upper valve voltage reference value (u*_(pj2)) and the lower valvevoltage reference value (u*_(nj2)) can be expressed as Equations (49)and (50), respectively.

$\begin{matrix}{u_{{pj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - \left\{ {{P\left( {err}_{{pj}\; 2} \right)} + {R_{1}\left( {err}_{{pj}\; 2} \right)} + {R_{2}\left( {err}_{{pj}\; 2} \right)}} \right\} - \left\{ {{L_{s}{\overset{\prime}{i}}_{{pj}\; 2}^{*}} - {L_{s}{\hat{l}}_{{pj}\; 2}}} \right\}}} & (49) \\{u_{{nj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - \left\{ {{P\left( {err}_{{nj}\; 2} \right)} + {R_{1}\left( {err}_{{nj}\; 2} \right)} + {R_{2}\left( {err}_{{nj}\; 2} \right)}} \right\} - \left\{ {{L_{s}{\overset{\prime}{i}}_{{nj}\; 2}^{*}} - {L_{s}{\hat{l}}_{{nj}\; 2}}} \right\}}} & (50)\end{matrix}$

If Equations (49) and (50) are simplified to design a controller,Equations (51) and (52) can be obtained.

$\begin{matrix}{u_{{pj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - \left\{ {{P\left( {err}_{{pj}\; 2} \right)} + {R_{1}\left( {err}_{{pj}\; 2} \right)} + {R_{2}\left( {err}_{{pj}\; 2} \right)}} \right\} + \left\{ {L_{s}{\hat{l}}_{{pj}\; 2}} \right\}}} & (51) \\{u_{{nj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} + E_{sj}} \right) - \left\{ {{P\left( {err}_{{nj}\; 2} \right)} + {R_{1}\left( {err}_{{nj}\; 2} \right)} + {R_{2}\left( {err}_{{nj}\; 2} \right)}} \right\} + {\left\{ {L_{s}{\hat{l}}_{{nj}\; 2}} \right\}.}}} & (52)\end{matrix}$

FIG. 5 is a view illustrating an internal configuration of a drivingapparatus and method for a modular multi-level converter according to anexemplary embodiment of the present invention, where three upper valvesare controlled.

As shown in FIG. 5, a driving apparatus 20 for a modular multi-levelconverter that controls an upper valve may include a proportionalcontroller 21, a first resonant-type current controller 22, a secondresonant-type current controller 23, and a compensator 24.

The driving apparatus 20 for the modular multi-level converter mayreceive a current reference value and a value of a current flowing inthe upper valve, and may obtain a difference therebetween to apply thedifference to the proportional controller 21, the first resonant-typecurrent controller 22, the second resonant-type current controller 23,and the compensator 24.

The outputted calculation values may be added up, and a voltagereference value may be generated by subtracting the sum from a voltagedifference value between a DC link voltage value and a system voltagevalue.

Based on this voltage reference value, the number of submodules to beturned on and submodules may be selected from the upper valve, and apulse width modulation signal may be applied to the submodules to drivethe submodules.

Thus, the driving apparatus for the modular multi-level converter maydirectly measure the current value from the upper valve of the valvebranch of a multi-level converter taking charge of one phase and mayreceive the current reference value to generate the voltage referencevalue. Accordingly, submodules to be driven may be selected and drivenfrom the corresponding upper valve without a help of an uppercontroller.

FIG. 6 is a view illustrating an internal configuration of a drivingapparatus and method for a modular multi-level converter according to anexemplary embodiment of the present invention, where three lower valvesare controlled.

Similarly to the driving apparatus for the modular multi-level convertercontrolling the upper valve, a driving apparatus 20 for a modularmulti-level converter controlling the lower valve may also include aproportional controller 21, a first resonant-type current controller 22,a second resonant-type current controller 23, and a compensator 24.

The driving apparatus 20 for the modular multi-level converter takingcharge of the lower valve may receive a current reference value and avalue of a current flowing in the upper valve, and may obtain adifference therebetween to apply the difference to the proportionalcontroller 21, the first resonant-type current controller 22, the secondresonant-type current controller 23, and the compensator 24.

The outputted calculation values may be added up, and a voltagereference value may be generated by subtracting the sum from a sum of aDC link voltage value and a system voltage value.

Based on this voltage reference value, the number of submodules to beturned on and submodules may be selected from the upper valve, and apulse width modulation signal may be applied to the submodules to drivethe submodules.

FIG. 7 is a view illustrating a simplified example of the drivingapparatus for the modular multi-level converter of FIG. 5.

The driving apparatus for the modular multi-level converter shown inFIG. 7 may be configured to exclude the compensator 24 from thecomponents of the driving apparatus for the modular multi-levelconverter shown in FIG. 5.

The modular multi-level converter of FIG. 7 can reduce the amount ofoperation by omitting the compensator 24.

Accordingly, a user who uses the driving apparatus and method for themodular multi-level converter may also design so as to additionallyinclude the compensator 24 to generate a more accurate valve voltagereference value. On the other hand, a user who prefers speed to accuracymay select the simplified driving apparatus for the modular multi-levelconverter that omits the compensator 24.

FIG. 8 is a view illustrating a simplified example of the drivingapparatus for the modular multi-level converter of FIG. 6.

The driving apparatus for the modular multi-level converter shown inFIG. 8 may also be configured to exclude the compensator 24 from thecomponents of the driving apparatus for the modular multi-levelconverter shown in FIG. 6.

The driving apparatus 20 for the modular multi-level converter 20 mayobtain a difference between a current reference value of the lower valveand a measured value of a current flowing in the lower valve and mayobtain an sum of values calculated by passing the error value throughthe proportional controller 21, the first resonant-type currentcontroller 22, and the second resonant-type current controller 23.

Thereafter, the driving apparatus 20 for the modular multi-levelconverter 20 may generated a voltage reference value applied to thelower valve, by subtracting the sum of values calculated by passingthrough the proportion controller 21, the first resonant-type currentcontroller 22, and the second resonant-type current controller 23 from asum of a half of the DC link voltage and the system voltage.

FIG. 9 is a view illustrating an estimator added to the drivingapparatus for the modular multi-level converter of FIG. 7.

A driving apparatus 20 for a modular multi-level converter may furtherinclude an estimator 25. The estimator 25 may calculate a parametervariation value due to a magnitude variation of circulating currentsuppression inductor and resistor components of the driving apparatus 20for the modular multi-level converter.

The estimator 25 may amplify an error value between the currentreference value and the measured current value using a predeterminedtuning parameter

FIG. 10 is a view illustrating an estimator added to the drivingapparatus for the modular multi-level converter of FIG. 8.

Similarly to FIG. 9, a driving apparatus 20 for a modular multi-levelconverter may further include an estimator 25. The estimator 25 maycalculate a parameter variation value due to a magnitude variation ofcirculating current suppression inductor and resistor components of thedriving apparatus 20 for the modular multi-level converter.

Also, the driving apparatus 20 for the modular multi-level converter maysubtract a calculated value of the estimator 25 from a sum of valuesoutputted from the proportional controller 21, the first resonant-typecurrent controller 22, and the second resonant-type current controller23.

A voltage reference value of the lower valve of the driving apparatus 20for the modular multi-level converter may be generated by subtractingthe foregoing calculated value from a sum of a half of the DC linkvoltage value and the system voltage value.

FIG. 11 is a view illustrating a relationship between a drivingapparatus for a modular multi-level converter and an upper controllerthereover according to an exemplary embodiment of the present invention.

Unlike a typical controller, an upper controller 30 of the drivingapparatus for the modular multi-level converter may serve to calculateonly a reference current value to be applied to the upper valve and areference current value to be applied to the lower valve. Detailcalculation may be performed by the driving apparatus 20 for the modularmulti-level converter.

Specifically, a value to suppress the circulating current may beobtained using the proportional controller 21, the first resonant-typecurrent controller 22 and the second resonant-type current controller23, and an error due to a parameter variation may be obtained using thesgn function. Thus, a voltage reference value to be used in the drivingapparatus and method for the modular multi-level converter may begenerated using the forgoing obtained values. Also, the number ofsubmodules may be determined, and a pulse width modulation signal may beapplied to each submodule that is selected. That is, since mostcalculation is performed by unit of valve, frequent data exchangebetween the controller 30 and the valve controller can be omitted.Accordingly, distributed control can be achieved.

FIG. 12 is a view illustrating a pulse width modulation signal appliedto a driving apparatus for a modular multi-level converter according toan exemplary embodiment of the present invention.

In FIG. 12, it can be confirmed that a pulse width modulation signalcorresponding to the voltage reference value calculated through theforegoing processes is applied to each submodule of a correspondingvalve unit.

The term “valve unit” refers to an upper valve or a lower valve of thevalve branch taking charge of one phase of the AC system.

Accordingly, the pulse width modulation signals applied to each valveunit may differ from each other in pulse width. Also, a pulse widthsignal generated by the valve controller according to the voltagereference value may be applied according to the situation of each valveunit

Hereinafter, effects of the driving apparatus and method for the modularmulti-level converter according to the exemplary embodiment of thepresent invention will be described with reference to graphs below.

FIG. 13 is a graph illustrating values measured in each system and DClink when a circulating current is not suppressed in a typicalmulti-level converter.

FIG. 13 shows (a) a value of system voltage, (b) a value of an AC systemcurrent of the modular multi-level converter, and (c) a circulatingcurrent flowing through a valve in the d-q frame, and shows (d) acirculating current flowing through a valve in the stationary referenceframe. Also, FIG. 13 shows (e) a value of a DC link current and (f) avalue of active power.

As shown in FIG. 13, when the system has an unbalance voltage, aharmonic component may rapidly increase in the circulating currentflowing inside the converter, making it difficult to ensure an operationwithin a stable current limit. Also, since a harmonic component severelyoccurs in a current of the DC system, the transmission quality may bedeteriorated.

Also, it can be seen that the quality is deteriorated due to a rapidincrease of the harmonic component in a value of active power of the ACsystem.

FIG. 14 is a graph illustrating results of control using the method ofQingrui Tu (2012) when an unbalance state occurs in a typicalmulti-level converter.

FIG. 14 shows (a) a value of system voltage, (b) a value of an AC systemcurrent of the modular multi-level converter, and (c) a circulatingcurrent flowing through a valve in the stationary reference frame, andshows (d) a circulating current flowing through a valve in the d-qframe. Also, FIG. 14 shows (e) a value of active power of the AC system,(f) a value of a current of the DC link, and (g) a value of a voltageapplied to the submodule.

Compared to FIG. 13, when the method of FIG. 14 is used, it can be seenthat the harmonic characteristics were slightly improved but thecirculating current was not completely removed as shown in FIGS. 14C and14D. Also, transient state characteristics may not be good, and theharmonics may be much included even at a stationary state. Since ripplesare also severely formed in a current of the DC link, it can be seenthat control is performed while much harmonic component is stillincluded.

On the other hand, the driving apparatus and method for the modularmulti-level converter according to the exemplary embodiment of thepresent invention can fully control the harmonic components included inthe circulating current, the AC system or DC link regardless of theunbalance voltage condition.

FIG. 15 is a view illustrating a configuration of a modular multi-levelconverter using a driving method of the modular multi-level converteraccording to an exemplary embodiment of the present invention, and FIG.16 is a view illustrating values of parameters to be used in a drivingapparatus and method for a modular multi-level converter according to anexemplary embodiment of the present invention.

FIG. 17 is a graph illustrating results of control by a drivingapparatus and method for a modular multi-level converter according to anexemplary embodiment of the present invention.

FIG. 17 shows (a) a system voltage, (b) an AC system current of themodular multi-level converter, and (c) a circulating current flowing ina valve branch in the stationary reference frame, and shows (d) acirculating current flowing in the valve branch in the d-q frame. Also,FIG. 17 shows (e) active power of the AC system, (f) a current of the DClink, and (g) a voltage applied to the submodule.

As shown in FIGS. 13 and 14, when one phase among 3-phase system voltageis grounded, a typical method shows oscillation characteristics up anddown, and thus is not good in transient state characteristics andstationary state characteristics regarding control of the circulatingcurrent.

However, as shown in FIGS. 17C and 17D, it can be seen that the drivingapparatus and method for the modular multi-level converter according tothe exemplary embodiment of the present invention shows excellentresponse and convergence of the circulating current.

Also, while a typical method is not good in the transient statecharacteristics of the DC link current and includes a harmonic componenteven in the stationary state, it can be seen that the driving method forthe modular multi-level converter according to the exemplary embodimentof the present invention shows significant improvement in both transientstate characteristics and stationary state characteristics as shown inFIG. 17F.

In terms of active power control, while a typical method shows that theactive power has a harmonic component, it can be seen that the drivingapparatus and method for the modular multi-level converter according tothe exemplary embodiment of the present invention shows that theharmonic component is completely removed as shown in FIG. 17E.

Accordingly, regardless of 3-phase balance or 3-phase unbalance state ofthe system power, the present invention can completely remove theharmonic components of the active power and the circulating current.

FIG. 18 is a view illustrating a valve current and a reference value ofthe valve current of the driving apparatus and method for the modularmulti-level converter of FIG. 17.

Even under the unbalance voltage condition, it can be seen that thedriving apparatus and method for the modular multi-level converteraccording to the exemplary embodiment of the present invention allowsthe current value applied to the valve to be accurately converged to thevalve current reference value.

As described above, a driving apparatus and method for a modularmulti-level has the following effects

First, six valves constituting a HVDC transmission system including amodular multi-level converter can be separately controlled.

In a typical driving method for a modular multi-level converter, since acurrent controller and a circulating current suppression controller areimplemented with a 3-phase parameter, roles of six valve controller arelimited to the number and sorting operation of submodules and thetriggering of the submodules.

However, in the driving method for the modular multi-level converteraccording to the exemplary embodiment of the present invention, all ofthe current controller, the circulating current suppression controller,the calculation of the number of submodules, sorting, and triggering ofsubmodules can be performed in the valve controller. That is, six valvecontrollers can be independently operated, and parallel processing canbe performed.

Second, since implemented in the stationary reference frame, parametersneed not be converted into the d-q frame, and a notch filter need not beused to remove noise included in signals of the d-q frame.

Also, in a typical driving method for a modular multi-level converter,since a method of measuring a circulating current and then allowing thecirculating current to be “0” is used, a circulating current componentneeds to be calculated. However, in the driving method for the modularmulti-level converter, since the circulating current can be suppressedby applying a method of simply suppressing an error harmonic signalcorresponding to a half of the AC-grid frequency, the circulatingcurrent parameter need not be known. Accordingly, when the drivingmethod for the modular multi-level converter is applied to the HVDCtransmission method, the processing speed can be significantly improved.

Third, an AC component of the circulating current can be completelysuppressed. Accordingly, a harmonic component included in a DC linkcurrent can be completely removed, and a harmonic component of an activepower component flowing in an AC system can be completely removed.

Fourth, although an inductor and a resistor including in the valvecontroller vary within a limited magnitude or a manufacturing error or adisturbance occurs, suppression can be immediately performed.Accordingly, the present invention is advantageous in terms of theparameter variation and the signal disturbance.

The invention has been described in detail with reference to exemplaryembodiments thereof. However, it will be appreciated by those skilled inthe art that changes may be made in these embodiments without departingfrom the principles and spirit of the invention, the scope of which isdefined in the appended claims and their equivalents.

1. A driving method for a modular multi-level converter that converts analternating current (AC) into a direct current (DC) or converts a DCinto an AC using the modular multi-level converter with a plurality ofsubmodules stacked to deliver power in an AC system, the modularmulti-level converter comprising a plurality of valves independentlydriven and an upper valve that is one of valve branches comprising thevalves, the method comprising: inputting a current reference value(i*_(pj2)) of the upper valve of the modular multi-level converter;measuring a current value (i_(pj2)) of the valve; calculating an errorvalue (err_(pj2)) between the current reference value and the measuredcurrent value of the upper valve; measuring a DC link voltage value(V_(dc2)) of the modular multi-level converter; measuring the AC-gridvoltage value (E_(sj)) of the modular multi-level converter; andcalculating a voltage reference value (u*_(pj2)) of the upper valveusing the current reference value (i*_(pj2)), the measured current value(i_(pj2)), the error value (err_(pj2)), the DC link voltage value(v_(dc2)), and the AC-grid voltage value (E_(sj)).
 2. The driving methodof claim 1, further comprising calculating a parameter variation value({circumflex over (l)}_(pj2)) of a circulating current suppressioninductor of the modular multi-level converter between the measuring ofthe AC-grid voltage value (E_(sj)) of the modular multi-level converterand calculating of the voltage reference value (u*_(pj2)) of the uppervalve using the current reference value, the measured current value, theerror value, the DC link voltage value, and the system voltage value. 3.The driving method of claim 2, wherein the calculating of the parametervariation value ({circumflex over (l)}_(pj2)) of a circulating currentsuppression inductor of the modular multi-level converter comprises:obtaining a differential value of the parameter variation value of thecirculating current suppression inductor using the following equation:{acute over ({circumflex over (l)}_(pj2) =−m ₁ err _(pj2); andintegrating the differential value of the parameter variation value ofthe circulating current suppression inductor, wherein m₁ is apredetermined tuning constant.
 4. The driving method of claim 2, whereinthe calculating of the voltage reference value (u*_(pj2)) of the uppervalve using the current reference value (i*_(pj2)), the measured currentvalue (i_(pj2)), the error value (err_(pj2)), the DC link voltage value(V_(dc2)), the AC-grid voltage value (E_(sj)), and the parametervariation value ({circumflex over (l)}_(pj2)) of the circulating currentsuppression inductor comprises calculating the voltage reference value(u*_(pj2)) of the upper valve using the following equation:$u_{{pj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - \left\{ {{P\left( {err}_{{pj}\; 2} \right)} + {R_{1}\left( {err}_{{pj}\; 2} \right)} + {R_{2}\left( {err}_{{pj}\; 2} \right)}} \right\} + {\left\{ {L_{s}{\hat{l}}_{{pj}\; 2}} \right\}.}}$5. The driving method of claim 2, wherein the calculating of the voltagereference value (u*_(pj2)) of the upper valve using the currentreference value (i*_(pj2)), the measured current value (i_(pj2)), theerror value (err_(pj2)), the DC link voltage value (V_(dc2)), theAC-grid voltage value (E_(sj)), and the parameter variation value({circumflex over (l)}_(pj2)) of the circulating current suppressioninductor comprises calculating the voltage reference value (u*_(pj2)) ofthe upper valve using the following equation:$u_{{pj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - \left\{ {{P\left( {err}_{{pj}\; 2} \right)} + {R_{1}\left( {err}_{{pj}\; 2} \right)} + {R_{2}\left( {err}_{{pj}\; 2} \right)}} \right\} - \left\{ {{L_{s}i_{{pj}\; 2}^{*}} - {L_{s}{\hat{l}}_{{pj}\; 2}}} \right\}}$6. The driving method of claim 1, wherein the calculating of the voltagereference value (u*_(pj2)) of the upper valve using the currentreference value (i*_(pj2)), the measured current value (i_(pj2)), theerror value (err_(pj2)), the DC link voltage value (V_(dc2)), and theAC-grid voltage value (E_(sj)) comprises calculating the voltagereference value (u*_(pj2)) of the upper valve using the followingequation:$u_{{pj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - {\left\{ {{P\left( {err}_{{pj}\; 2} \right)} + {R_{1}\left( {err}_{{pj}\; 2} \right)} + {R_{2}\left( {err}_{{pj}\; 2} \right)}} \right\}.}}$7. The driving method of claim 1, wherein the calculating of the voltagereference value (u*_(pj2)) of the upper valve using the currentreference value (i*_(pj2)), the measured current value (i_(pj2)), theerror value (err_(pj2)), the DC link voltage value (V_(dc2)), theAC-grid voltage value (E_(sj)), and an sgn function comprisescalculating the voltage reference value (u*_(pj2)) of the upper valveusing the following equation:$u_{{pj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - \left\{ {{P\left( {err}_{{pj}\; 2} \right)} + {R_{1}\left( {err}_{{pj}\; 2} \right)} + {R_{2}\left( {err}_{{pj}\; 2} \right)}} \right\} - \left\{ {\rho_{{pj}\; 2}{{sgn}\left( {err}_{{pj}\; 2} \right)}} \right\}}$wherein the sign function denotes a sign function operated by thefollowing equations:sgn(err _(pj2))=1(err _(pj2)>0)sgn(err _(pj2))=0(err _(pj2)≦0) and ρ_(pj2) denotes a proportional gain.8. The driving method of claim 1, wherein the calculating of the voltagereference value (u*_(pj2)) using the current reference value (i*_(pj2)),the measured current value (i_(pj2)), the error value (err_(pj2)), theDC link voltage value (V_(dc2)), the AC-grid voltage value (E_(sj)), andan sgn function comprises calculating the voltage reference value(u*_(pj2)) of the upper valve using the following equation:$u_{{pj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} - E_{sj}} \right) - \left\{ {{P\left( {err}_{{pj}\; 2} \right)} + {R_{1}\left( {err}_{{pj}\; 2} \right)} + {R_{2}\left( {err}_{{pj}\; 2} \right)}} \right\} - \left\{ {\rho_{{pj}\; 2}{{sgn}\left( {err}_{{pj}\; 2} \right)}} \right\}}$wherein: the sign function denotes a sign function operated by thefollowing equations:sgn(err _(pj2))=1(err _(pj2)>0)sgn(err _(pj2))=0(err _(pj2)≦0) ρ_(pj2) denotes a proportional gain; andL_(s) denotes a circulating current suppression inductor of the uppervalve.
 9. The driving method of claim 4, wherein P(err_(pj2)),R₁(err_(pj2)), and R₂(err_(pj2)) are calculated using the followingequations: P(err_(pj 2)) = (K_(p))err_(pj 2)${{R_{1}\left( {err}_{{pj}\; 2} \right)} = {\left( \frac{K_{i\; 1}s}{s^{2} + \left( \omega_{o} \right)^{2}} \right){err}_{{pj}\; 2}}},{and}$${{R_{2}\left( {err}_{{pj}\; 2} \right)} = {\left( \frac{K_{i\; 2}s}{s^{2} + \left( {2\omega_{o}} \right)^{2}} \right){err}_{{pj}\; 2}}},$wherein K_(p), K_(i1), and K_(i2) denote predetermined gain values, andω_(o) denotes a AC-grid frequency.
 10. The driving method of claim 1,wherein the inputting of the current reference value (i*_(pj2)) of theupper valve of the modular multi-level converter comprises calculatingthe current reference value (i*_(pj2)) using the following equation:${i_{{pj}\; 2}^{*} = {\frac{i_{{dc}\; 2}^{*}}{3} + {\frac{i_{sj}^{*}}{2}\mspace{14mu} \left( {{j = a},b,c} \right)}}},$and i*_(dc2) denotes a DC current reference value flowing in a DC systemand i*_(sj) denotes a reference value regarding a phase current.
 11. Thedriving method of claim 10, wherein the reference value regarding thephase current is calculated into an expression of a stationary referenceframe using the following equation: ${\begin{bmatrix}i_{sa}^{*} \\i_{sb}^{*} \\i_{sc}^{*}\end{bmatrix} = {\begin{bmatrix}1 & 0 \\{- \frac{1}{2}} & \frac{\sqrt{3}}{2} \\{- \frac{1}{2}} & {- \frac{\sqrt{3}}{2}}\end{bmatrix}\begin{bmatrix}i_{s\; \alpha}^{*} \\i_{s\; \beta}^{*}\end{bmatrix}}},$ and i*_(sα) and i*_(sβ) denote the reference valueregarding the phase current expressed into a rotating stationaryreference frame.
 12. The driving method of claim 11, wherein: i*_(sα)and i*_(sβ) convert an expression of the reference value regarding thephase current at a d-q frame into the rotating stationary referenceframe using the following equation:i* _(sαβ) =i _(sdq) ^(p*) e ^(jωt) +i _(sdq) ^(n*) e ^(−jωt); i_(sdq)^(p*) is an abbreviation of a d-axis and a q-axis (i_(sq) ^(p*),i_(sd)^(p*)) of a positive sequence component current reference value; i_(sdq)^(n*) is an abbreviation of a d-axis and a q-axis (i_(sq) ^(n*),i_(sd)^(n*)) of a negative sequence component current reference value; i_(sd)^(p*) denotes the d-axis of the positive sequence component currentreference value; i_(sq) ^(p*) denotes the q-axis of the positivesequence component current reference value; i_(sd) ^(n*) denotes thed-axis of the negative sequence component current reference value;i_(sq) ^(n*) denotes the q-axis of the negative sequence componentcurrent reference value; i_(sq) ^(p*), i_(sd) ^(p*), i_(sq) ^(n*), andi_(sd) ^(n*) are calculated using the following equations:${i_{sq}^{p^{*}} = {{PI}\left( {P_{s}^{*} - P_{s}} \right)}},{i_{sd}^{p^{*}} = {{PI}\left( {Q_{s}^{*} - Q_{s}} \right)}},{i_{sq}^{n^{*}} = {{{- \frac{E_{sd}^{n}}{E_{sq}^{p}}}i_{sd}^{p}} - {\frac{E_{sq}^{n}}{E_{sq}^{p}}i_{sq}^{p}}}},{and}$${i_{sd}^{n^{*}} = {{\frac{E_{sq}^{n}}{E_{sq}^{p}}i_{sd}^{p}} - {\frac{E_{sd}^{n}}{E_{sq}^{p}}i_{sq}^{p}}}};$and P_(s) denotes active power in the AC system, P*_(s) denotes areference value of active power in the AC system, Q_(s) denotes reactivepower in the AC system, Q*_(s) denotes a reference value of reactivepower in the AC system, E_(sd) ^(p) denotes a d-axis voltage of apositive sequence voltage flowing in the AC system, E_(sq) ^(p) denotesa q-axis voltage of a positive sequence voltage flowing in the ACsystem, E_(sd) ^(n) denotes a d-axis voltage of a negative sequencevoltage flowing in the AC system, and E_(sq) ^(n) denotes a q-axisvoltage of a negative sequence voltage flowing in the AC system.
 13. Thedriving method of claim 10, wherein the reference value (i*_(dc2)) ofthe DC system is calculated using the following equation:${i_{{dc}\; 2}^{*} = {\frac{3}{2}\left( \frac{E_{sq}^{p}}{V_{{dc}\; 2}} \right)i_{sq}^{p^{*}}}},$and E_(sq) ^(p) denotes a q-axis voltage of a positive sequencecomponent voltage flowing in the AC system and i_(sq) ^(p*) denotes aq-axis current of a positive sequence component current reference valueflowing in the AC system.
 14. The driving method of claim 1, after thecalculating of the voltage reference value (u*_(pj2)) using the currentreference value (i*_(pj2)), the measured current value (i_(pj2)), theerror value (err_(pj2)), the DC link voltage value (V_(dc2)), and theAC-grid voltage value (E_(sj)), comprising: calculating the number ofsubmodules to be triggered among submodules of the upper valve;selecting submodules corresponding to the number of submodules; andapplying a pulse width modulation signal to the selected submodules. 15.A driving method for a modular multi-level converter that converts analternating current (AC) into a direct current (DC) or converts a DCinto an AC using the modular multi-level converter with a plurality ofsubmodules stacked to deliver power in an AC system, the modularmulti-level converter comprising a plurality of valves independentlydriven and a lower valve that is one of valve branches comprising thevalves, the method comprising: inputting a current reference value(i*_(nj2)) of the lower valve of the modular multi-level converter;measuring a current value (i_(nj2)) of the valve; calculating an errorvalue (err_(nj2)) between the current reference value and the measuredcurrent value of the lower valve; measuring a DC link voltage value(V_(dc2)) of the modular multi-level converter; measuring a AC-gridvoltage value (E_(sj)) of the modular multi-level converter; andcalculating a voltage reference value (u*_(pj2)) using the currentreference value (i*_(nj2)), the measured current value (i_(nj2)), theerror value (err_(nj2)), the DC link voltage value (V_(dc2)), and theAC-grid voltage value (E_(sj)).
 16. The driving method of claim 15,further comprising calculating a parameter variation value ({circumflexover (l)}_(nj2)) of a circulating current suppression inductor of themodular multi-level converter between the measuring of the AC-gridvoltage value (E_(sj)) of the modular multi-level converter andcalculating of the voltage reference value (u*_(nj2)) using the currentreference value, the measured current value, the error value, the DClink voltage value, and the system voltage value.
 17. The driving methodof claim 15, wherein the calculating of the parameter variation value({circumflex over (l)}_(nj2)) of a circulating current suppressioninductor of the modular multi-level converter comprises: obtaining adifferential value of the parameter variation value of the circulatingcurrent suppression inductor using the following equation:{acute over ({circumflex over (l)}_(nj2) =−m ₂ err _(nj2); andintegrating the differential value of the parameter variation value ofthe circulating current suppression inductor, wherein m₂ is apredetermined tuning constant.
 18. The driving method of claim 16,wherein the calculating of the voltage reference value (u*_(nj2)) of thelower valve using the current reference value (i*_(nj2)), the measuredcurrent value (i_(nj2)), the error value (err_(nj2)), the DC linkvoltage value (V_(dc2)), the AC-grid voltage value (E_(sj)), and theparameter variation value ({circumflex over (l)}_(nj2)) of the inductorcomprises calculating the voltage reference value (u*_(nj2)) of thelower valve using the following equation:$u_{{nj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} + E_{sj}} \right) - \left\{ {{P\left( {err}_{{nj}\; 2} \right)} + {R_{1}\left( {err}_{{nj}\; 2} \right)} + {R_{2}\left( {err}_{{nj}\; 2} \right)}} \right\} + \left\{ {L_{s}{\hat{l}}_{{nj}\; 2}} \right\}}$19. The driving method of claim 16, wherein the calculating of thevoltage reference value (u*_(nj2)) of the lower valve using the currentreference value (i*_(nj2)), the measured current value (i_(nj2)), theerror value (err_(nj2)), the DC link voltage value (V_(dc2)), theAC-grid voltage value (E_(sj)), and the parameter variation value({circumflex over (l)}_(nj2)) of the inductor comprises calculating thevoltage reference value (u*_(nj2)) of the lower valve using thefollowing equation:$u_{{nj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} + E_{sj}} \right) - \left\{ {{P\left( {err}_{{nj}\; 2} \right)} + {R_{1}\left( {err}_{{nj}\; 2} \right)} + {R_{2}\left( {err}_{{nj}\; 2} \right)}} \right\} + \left\{ {{L_{s}i_{{nj}\; 2}^{*}} - {L_{s}{\hat{l}}_{{nj}\; 2}}} \right\}}$20. The driving method of claim 15, wherein the calculating of thevoltage reference value (u*_(nj2)) of the lower valve using the currentreference value (i*_(nj2)), the measured current value (i_(nj2)), theerror value (err_(nj2)), the DC link voltage value (V_(dc2)), and theAC-grid voltage value (E_(sj)) comprises calculating the voltagereference value (u*_(nj2)) of the lower valve using the followingequation:$u_{{nj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} + E_{sj}} \right) - \left\{ {{P\left( {err}_{{nj}\; 2} \right)} + {R_{1}\left( {err}_{{nj}\; 2} \right)} + {R_{2}\left( {err}_{{nj}\; 2} \right)}} \right\}}$21. The driving method of claim 15, wherein the calculating of thevoltage reference value (u*_(nj2)) of the lower valve using the currentreference value (i*_(nj2)), the measured current value (i_(nj2)), theerror value (err_(nj2)), the DC link voltage value (V_(dc2)), theAC-grid voltage value (E_(sj)), and an sgn function comprisescalculating the voltage reference value (u*_(nj2)) of the lower valveusing the following equation:${u_{{nj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} + E_{sj}} \right) - \left\{ {{P\left( {err}_{{nj}\; 2} \right)} + {R_{1}\left( {err}_{{nj}\; 2} \right)} + {R_{2}\left( {err}_{{nj}\; 2} \right)}} \right\} - \left\{ {\rho_{{nj}\; 2}{{sgn}\left( {err}_{{nj}\; 2} \right)}} \right\}}},$wherein the sign function denotes a sign function operated by thefollowing equations:sgn(err _(nj2))=1(err _(nj2)>0)sgn(err _(nj2))=0(err _(nj2)≦0) and ρ_(nj2) denotes a proportional gain.22. The driving method of claim 15, wherein the calculating of thevoltage reference value (u*_(nj2)) of the lower valve using the currentreference value (i*_(nj2)), the measured current value (i_(nj2)), theerror value (err_(nj2)), the DC link voltage value (V_(dc2)), theAC-grid voltage value (E_(sj)), and an sgn function comprisescalculating the voltage reference value (u*_(nj2)) of the lower valveusing the following equation:${u_{{nj}\; 2}^{*} = {\left( {\frac{V_{{dc}\; 2}}{2} + E_{sj}} \right) - \left\{ {{P\left( {err}_{{nj}\; 2} \right)} + {R_{1}\left( {err}_{{nj}\; 2} \right)} + {R_{2}\left( {err}_{{nj}\; 2} \right)}} \right\} - \left\{ {{L_{s}i_{{nj}\; 2}^{*}} + {\rho_{{nj}\; 2}{{sgn}\left( {err}_{{nj}\; 2} \right)}}} \right\}}},$wherein the sign function denotes a s¹ign function operated by thefollowing equations:sgn(err _(nj2))=1(err _(nj2)>0)sgn(err _(nj2))=0(err _(nj2)≦0) ρ_(nj2) denotes a proportional gain; andL_(s) denotes a circulating current suppression inductor of the uppervalve.
 23. The driving method of claim 19, wherein P(err_(nj2)),R₁(err_(nj2)), and R₂(err_(nj2)) are calculated using the followingequations:${{P\left( {err}_{{nj}\; 2} \right)} = {\left( K_{p} \right){err}_{{nj}\; 2}}},{{R_{1}\left( {err}_{{nj}\; 2} \right)} = {\left( \frac{K_{i\; 1}s}{s^{2} + \left( \omega_{0} \right)^{2}} \right){err}_{{nj}\; 2}}},{and}$${{R_{2}\left( {err}_{{nj}\; 2} \right)} = {\left( \frac{K_{i\; 2}s}{s^{2} + \left( {2\omega_{0}} \right)^{2}} \right){err}_{{nj}\; 2}}},$wherein K_(p), K_(i1), and K_(i2) denote predetermined gain values, andω_(o) denotes a AC-grid frequency.
 24. The driving method of claim 15,wherein the inputting of the current reference value (i*_(nj2)) of theupper valve of the modular multi-level converter comprises calculatingthe current reference value (i*_(nj2)) using the following equation:${i_{{nj}\; 2}^{*} = {\frac{i_{{dc}\; 2}^{*}}{3} - \frac{i_{sj}^{*}}{2}}},$and i*_(dc2) denotes a DC current reference value flowing in a DC systemand i*_(sj) denotes a reference value regarding a phase current.
 25. Thedriving method of claim 24, wherein the reference value regarding thephase current is calculated into an expression of a stationary referenceframe using the following equation: ${\begin{bmatrix}i_{sa}^{*} \\i_{sb}^{*} \\i_{sc}^{*}\end{bmatrix} = {\begin{bmatrix}1 & 0 \\{- \frac{1}{2}} & \frac{\sqrt{3}}{2} \\{- \frac{1}{2}} & {- \frac{\sqrt{3}}{2}}\end{bmatrix}\begin{bmatrix}i_{s\; \alpha}^{*} \\i_{s\; \beta}^{*}\end{bmatrix}}},$ and i*_(sα) and i*_(sβ) denote the reference valueregarding the phase current expressed into a rotating stationaryreference frame.
 26. The driving method of claim 25, wherein: i*_(sα)and i*_(sβ) convert an expression of the reference value regarding thephase current at a d-q frame into the rotating stationary referenceframe using the following equation:i* _(sαβ) =i _(sdq) ^(p*) e ^(jωt) +i _(sdq) ^(n*) e ^(−jωt); i_(sdq)^(p*) is an abbreviation of a d-axis and a q-axis (i_(sq) ^(p*),i_(sd)^(p*)) of a positive sequence component current reference value; i_(sdq)^(n*) is an abbreviation of a d-axis and a q-axis (i_(sq) ^(n*),i_(sd)^(n*)) of a negative sequence component current reference value; i_(sd)^(p*) denotes the d-axis of the positive sequence component currentreference value; i_(sq) ^(p*) denotes the q-axis of the positivesequence component current reference value; i_(sd) ^(n*) denotes thed-axis of the negative sequence component current reference value;i_(sq) ^(n*) denotes the q-axis of the negative sequence componentcurrent reference value; i_(sq) ^(p*), i_(sd) ^(p*), i_(sq) ^(n*), andi_(sd) ^(n*) are calculated using the following equations:${i_{sq}^{p^{*}} = {{PI}\left( {P_{s}^{*} - P_{s}} \right)}},{i_{sd}^{p^{*}} = {{PI}\left( {Q_{s}^{*} - Q_{s}} \right)}},{i_{sq}^{n^{*}} = {{{- \frac{E_{sd}^{n}}{E_{sq}^{p}}}i_{sd}^{p}} - {\frac{E_{sq}^{n}}{E_{sq}^{p}}i_{sq}^{p}}}},{and}$${i_{sd}^{n^{*}} = {{\frac{E_{sq}^{n}}{E_{sq}^{p}}i_{sd}^{p}} - {\frac{E_{sd}^{n}}{E_{sq}^{p}}i_{sq}^{p}}}};$and P_(s) denotes active power in the AC system, P*_(s) denotes areference value of active power in the AC system, Q_(s) denotes reactivepower in the AC system, Q*_(s) denotes a reference value of reactivepower in the AC system, E_(sd) ^(p) denotes a d-axis voltage of apositive sequence voltage flowing in the AC system, E_(sq) ^(p) denotesa q-axis voltage of a positive sequence voltage flowing in the ACsystem, E_(sd) ^(n) a denotes a d-axis voltage of a negative sequencevoltage flowing in the AC system, and E_(sq) ^(n) denotes a q-axisvoltage of a negative sequence voltage flowing in the AC system.
 27. Thedriving method of claim 26, wherein the reference value (i*_(dc2)) ofthe DC system is calculated using the following equation:${i_{{dc}\; 2}^{*} = {\frac{3}{2}\left( \frac{E_{sq}^{p}}{V_{{dc}\; 2}} \right)i_{sq}^{p^{*}}}},$and E_(sq) ^(p) denotes a q-axis voltage of a positive sequencecomponent voltage flowing in the AC system and i_(sq) ^(p*) denotes aq-axis current of a positive sequence component current reference valueflowing in the AC system.
 28. The driving method of claim 15, after thecalculating of the voltage reference value (u*_(pj2)) using the currentreference value (i*_(pj2)), the measured current value (i_(pj2)), theerror value (err_(pj2)), the DC link voltage value (V_(dc2)), and theAC-grid voltage value (E_(sj)), comprising: calculating the number ofsubmodules to be triggered among submodules of the upper valve;selecting submodules corresponding to the number of submodules; andapplying a pulse width modulation signal to the selected submodules. 29.The driving method of claim 1, wherein the driving method for themodular multi-level converter is driven at a valve unit of the modularmulti-level converter.
 30. A driving apparatus for a modular multi-levelconverter, comprising: an input unit receiving a current reference valueof an upper valve of one valve branch of the modular multi-levelconverter; a current measuring unit for measuring a current value of theupper valve of the modular multi-level converter; a direct current (DC)link voltage measuring unit for measuring a voltage value of a DC linkof the modular multi-level converter; a system voltage measuring unitfor measuring a system voltage value of the modular multi-levelconverter; an error calculating unit for calculating an error valuebetween the current reference value received by the input unit and thecurrent value measured by the current measuring unit; a proportionalcontroller proportionally amplifying the error value calculated by theerror calculating unit; a first resonant-type current controllerreceiving the error value calculated by the error calculating unit toconverge an error current equal to a AC-grid frequency to zero; a secondresonant-type current controller receiving the error value calculated bythe error calculating unit to converge a harmonic error current abouttwo times larger than the AC-grid frequency to zero; and a voltagereference value calculating unit for calculating a voltage referencevalue of the upper valve of the one valve branch of the modularmulti-level converter using the values calculated by the DC link voltagemeasuring unit, the system voltage measuring unit, the proportionalcontroller, the first resonant-type current controller, and the secondresonant-type current controller.
 31. The driving apparatus of claim 30,further comprising: a submodule selecting unit for selecting the numberof submodules to be triggered and the submodules to be triggered, usingthe voltage reference value calculated by the voltage reference valuecalculating unit; and a pulse width modulation signal generating unitapplying a pulse width modulation signal to the submodules selected bythe submodule selecting unit.
 32. The driving apparatus of claim 30,wherein the proportional controller amplifies the error value calculatedby the error calculating unit to a gain value.
 33. The driving apparatusof claim 30, wherein the first resonant-type current controllermultiplies the error value calculated by the error calculating unit andthe following equation:$\frac{K_{i\; 1}s}{s^{2} + \left( \omega_{o} \right)^{2}}$ toconverge the error current to zero, and K_(i1) denotes a predeterminedgain value of the first resonant-type current controller and ω_(o)denotes the AC-grid frequency.
 34. The driving apparatus of claim 30,wherein the second resonant-type current controller multiplies the errorvalue calculated by the error calculating unit and the followingequation:$\frac{K_{i\; 2}s}{s^{2} + \left( {2\omega_{o}} \right)^{2}}$ toconverge the harmonic error current about two times larger than theAC-grid frequency to zero, and K_(i1) denotes a predetermined gain valueof the second resonant-type current controller and ω_(o) denotes theAC-grid frequency.
 35. The driving apparatus of claim 30, wherein thevoltage reference value calculating unit obtains a voltage difference bysubtracting the AC-grid voltage value measured by the system voltagemeasuring unit from a half of the voltage value measured by the DC linkvoltage measuring unit, and calculates the voltage reference value bysubtracting a sum of the calculated values outputted by the proportionalcontroller, the first resonant-type current controller, and the secondresonant-type current controller from the voltage difference.
 36. Thedriving apparatus of claim 30, further comprising a compensator reducingan error generated from the modular multi-level converter, wherein thecompensator obtains an sgn output value by inputting the error value ofthe error calculating unit into an sgn function and then calculates acompensation value by multiplying the sgn output value and aproportional gain of the sgn function, and the sgn function is a signfunction.
 37. The driving apparatus of claim 36, wherein the voltagereference value calculating unit further receives an output value of thecompensator to obtain a voltage difference by subtracting the AC-gridvoltage value measured by the system voltage measuring unit from a halfof the voltage value measured by the DC link voltage measuring unit, andcalculates the voltage reference value by subtracting a sum of thecalculated values outputted by the proportional controller, the firstresonant-type current controller, the second resonant-type currentcontroller, and the compensator from the voltage difference.
 38. Thedriving apparatus of claim 30, further comprising an estimator thatobtains a variation estimation value by multiplying and integrating theerror value calculated by the error calculating unit and a predeterminedtuning constant to remove dynamic characteristics due to a variation ofcirculating current suppression inductor and resistor components of themodular multi-level converter.
 39. The driving apparatus of claim 38,wherein the voltage reference value calculating unit further receives anestimation value of the estimator to obtain a voltage difference bysubtracting the AC-grid voltage value measured by the system voltagemeasuring unit from a half of the voltage value measured by the DC linkvoltage measuring unit, and calculates the voltage reference value bysubtracting a sum of the calculated values outputted by the proportionalcontroller, the first resonant-type current controller, the secondresonant-type current controller, the compensator, and the estimatorfrom the voltage difference.
 40. A driving apparatus for a modularmulti-level converter, comprising: an input unit receiving a currentreference value of a lower valve of one valve branch of the modularmulti-level converter; a current measuring unit for measuring a currentvalue of the lower valve of the modular multi-level converter; a directcurrent (DC) link voltage measuring unit for measuring a voltage valueof a DC link of the modular multi-level converter; a system voltagemeasuring unit for measuring a system voltage value of the modularmulti-level converter; an error calculating unit for calculating anerror value between the current reference value received by the inputunit and the current value measured by the current measuring unit; aproportional controller proportionally amplifying the error valuecalculated by the error calculating unit; a first resonant-type currentcontroller receiving the error value calculated by the error calculatingunit to converge an error current equal to a AC-grid frequency to zero;a second resonant-type current controller receiving the error valuecalculated by the error calculating unit to converge a harmonic errorcurrent about two times larger than the AC-grid frequency to zero; and avoltage reference value calculating unit for calculating a voltagereference value of the lower valve of the one valve branch of themodular multi-level converter using the values calculated by the DC linkvoltage measuring unit, the system voltage measuring unit, theproportional controller, the first resonant-type current controller, andthe second resonant-type current controller.
 41. The driving apparatusof claim 40, further comprising: a submodule selecting unit forselecting the number of submodules to be triggered and the submodules tobe triggered, using the voltage reference value calculated by thevoltage reference value calculating unit; and a pulse width modulationsignal generating unit applying a pulse width modulation signal to thesubmodules selected by the submodule selecting unit.
 42. The drivingapparatus of claim 40, wherein the proportional controller amplifies theerror value calculated by the error calculating unit to a gain value.43. The driving apparatus of claim 40, wherein the first resonant-typecurrent controller multiplies the error value calculated by the errorcalculating unit and the following equation:$\frac{K_{i\; 1}s}{s^{2} + \left( \omega_{o} \right)^{2}}$ toconverge the error current to zero, and K_(i1) denotes a predeterminedgain value of the first resonant-type current controller and ω_(o)denotes the AC-grid frequency.
 44. The driving apparatus of claim 40,wherein the second resonant-type current controller multiplies the errorvalue calculated by the error calculating unit and the followingequation:$\frac{K_{i\; 2}s}{s^{2} + \left( {2\omega_{o}} \right)^{2}}$ toconverge the harmonic error current about two times larger than theAC-grid frequency to zero, and K_(i2) denotes a predetermined gain valueof the second resonant-type current controller and ω_(o) denotes theAC-grid frequency.
 45. The driving apparatus of claim 40, wherein thevoltage reference value calculating unit obtains a voltage sum by addingthe AC-grid voltage value measured by the system voltage measuring unitto a half of the voltage value measured by the DC link voltage measuringunit, and calculates the voltage reference value by subtracting a sum ofthe calculated values outputted by the proportional controller, thefirst resonant-type current controller, and the second resonant-typecurrent controller from the voltage sum.
 46. The driving apparatus ofclaim 40, further comprising a compensator reducing an error generatedfrom the modular multi-level converter, wherein the compensator obtainsan sgn output value by inputting the error value of the errorcalculating unit into an sgn function and then calculates a compensationvalue by multiplying the sgn output value and a proportional gain of thesgn function, and the sgn function is a sign function.
 47. The drivingapparatus of claim 46, wherein the voltage reference value calculatingunit further receives an output value of the compensator to obtain avoltage sum by adding the AC-grid voltage value measured by the systemvoltage measuring unit to a half of the voltage value measured by the DClink voltage measuring unit, and calculates the voltage reference valueby subtracting a sum of the calculated values outputted by theproportional controller, the first resonant-type current controller, thesecond resonant-type current controller, and the compensator from thevoltage sum.
 48. The driving apparatus of claim 40, further comprisingan estimator that obtains a variation estimation value by multiplyingand integrating the error value calculated by the error calculating unitand a predetermined constant to remove dynamic characteristics due to avariation of circulating current suppression inductor and resistorcomponents of the modular multi-level converter.
 49. The drivingapparatus of claim 40, wherein the voltage reference value calculatingunit further receives an estimation value of the estimator to obtain avoltage sum by adding the AC-grid voltage value measured by the systemvoltage measuring unit to a half of the voltage value measured by the DClink voltage measuring unit, and calculates the voltage reference valueby subtracting a sum of the calculated values outputted by theproportional controller, the first resonant-type current controller, thesecond resonant-type current controller, the compensator, and theestimator from the voltage sum.
 50. The driving apparatus of claim 30,wherein the driving apparatus for the modular multi-level converter isdriven at a valve unit of the modular multi-level converter.
 51. Thedriving method of claim 5, wherein P(err_(pj2)), R₁(err_(pj2)), andR₂(err_(pj2)), are calculated using the following equations:P(err_(pj 2)) = (K_(p))err_(pj 2)${{R_{1}\left( {err}_{{pj}\; 2} \right)} = {\left( \frac{K_{i\; 1}s}{s^{2} + \left( \omega_{o} \right)^{2}} \right){err}_{{pj}\; 2}}},{and}$${{R_{2}\left( {err}_{{pj}\; 2} \right)} = {\left( \frac{K_{i\; 2}s}{s^{2} + \left( {2\omega_{o}} \right)^{2}} \right){err}_{{pj}\; 2}}},$wherein K_(p), K_(i1), and K_(i2) denote predetermined gain values, andω_(o) denotes a AC-grid frequency.
 52. The driving method of claim 6,wherein P(err_(pj2)), R₁(err_(pj2)), and R₂(err_(pj2)) are calculatedusing the following equations: P(err_(pj 2)) = (K_(p))err_(pj 2)${{R_{1}\left( {err}_{{pj}\; 2} \right)} = {\left( \frac{K_{i\; 1}s}{s^{2} + \left( \omega_{o} \right)^{2}} \right){err}_{{pj}\; 2}}},{and}$${{R_{2}\left( {err}_{{pj}\; 2} \right)} = {\left( \frac{K_{i\; 2}s}{s^{2} + \left( {2\omega_{o}} \right)^{2}} \right){err}_{{pj}\; 2}}},$wherein K_(p), K_(i1), and K_(i2) denote predetermined gain values, andω_(o) denotes a AC-grid frequency.
 53. The driving method of claim 7,wherein P(err_(pj2)), R₁(err_(pj2)), and R₂(err_(pj2)) are calculatedusing the following equations: P(err_(pj 2)) = (K_(p))err_(pj 2)${{R_{1}\left( {err}_{{pj}\; 2} \right)} = {\left( \frac{K_{i\; 1}s}{s^{2} + \left( \omega_{o} \right)^{2}} \right){err}_{{pj}\; 2}}},{and}$${{R_{2}\left( {err}_{{pj}\; 2} \right)} = {\left( \frac{K_{i\; 2}s}{s^{2} + \left( {2\omega_{o}} \right)^{2}} \right){err}_{{pj}\; 2}}},$wherein K_(p), K_(i1), and K_(i2) denote predetermined gain values, andω_(o) denotes a AC-grid frequency.
 54. The driving method claim 8,wherein P(err_(pj2)), R₁(err_(pj2)), and R₂(err_(pj2)) are calculatedusing the following equations: P(err_(pj 2)) = (K_(p))err_(pj 2)${{R_{1}\left( {err}_{{pj}\; 2} \right)} = {\left( \frac{K_{i\; 1}s}{s^{2} + \left( \omega_{o} \right)^{2}} \right){err}_{{pj}\; 2}}},{and}$${{R_{2}\left( {err}_{{pj}\; 2} \right)} = {\left( \frac{K_{i\; 2}s}{s^{2} + \left( {2\omega_{o}} \right)^{2}} \right){err}_{{pj}\; 2}}},$wherein K_(p), K_(i1) and K_(i2) denote predetermined gain values, andω_(o) denotes a AC-grid frequency.
 55. The driving method of claim 20,wherein P(err_(nj2)), R₁(err_(nj2)), and R₂(err_(nj2)) are calculatedusing the following equations:${{P\left( {err}_{{nj}\; 2} \right)} = {\left( K_{p} \right){err}_{{nj}\; 2}}},{{R_{1}\left( {err}_{{nj}\; 2} \right)} = {\left( \frac{K_{i\; 1}s}{s^{2} + \left( \omega_{o} \right)^{2}} \right){err}_{{nj}\; 2}}},{and}$${{R_{2}\left( {err}_{{nj}\; 2} \right)} = {\left( \frac{K_{i\; 2}s}{s^{2} + \left( {2\omega_{o}} \right)^{2}} \right){err}_{{nj}\; 2}}},$wherein K_(p), K_(i1) and K_(i2) denote predetermined gain values, andω_(o) denotes a AC-grid frequency.
 56. The driving method claim 21,wherein P(err_(nj2)), R₁(err_(nj2)), and R₂(err_(nj2)) are calculatedusing the following equations:${{P\left( {err}_{{nj}\; 2} \right)} = {\left( K_{p} \right){err}_{{nj}\; 2}}},{{R_{1}\left( {err}_{{nj}\; 2} \right)} = {\left( \frac{K_{i\; 1}s}{s^{2} + \left( \omega_{o} \right)^{2}} \right){err}_{{nj}\; 2}}},{and}$${{R_{2}\left( {err}_{{nj}\; 2} \right)} = {\left( \frac{K_{i\; 2}s}{s^{2} + \left( {2\omega_{o}} \right)^{2}} \right){err}_{{nj}\; 2}}},$wherein K_(p), K_(i1), and K_(i2) denote predetermined gain values, andω_(o) denotes a AC-grid frequency.
 57. The driving method claim 22,wherein P(err_(nj2)), R₁(err_(nj2)), and R₂(err_(nj2)) are calculatedusing the following equations:${{P\left( {err}_{{nj}\; 2} \right)} = {\left( K_{p} \right){err}_{{nj}\; 2}}},{{R_{1}\left( {err}_{{nj}\; 2} \right)} = {\left( \frac{K_{i\; 1}s}{s^{2} + \left( \omega_{o} \right)^{2}} \right){err}_{{nj}\; 2}}},{and}$${{R_{2}\left( {err}_{{nj}\; 2} \right)} = {\left( \frac{K_{i\; 2}s}{s^{2} + \left( {2\omega_{o}} \right)^{2}} \right){err}_{{nj}\; 2}}},$wherein K_(p), K_(i1), and K_(i2) denote predetermined gain values, andω_(o) denotes a AC-grid frequency.
 58. The driving method of claim 15,wherein the driving method for the modular multi-level converter isdriven at a valve unit of the modular multi-level converter.
 59. Thedriving apparatus of claim 40, wherein the driving apparatus for themodular multi-level converter is driven at a valve unit of the modularmulti-level converter.